Use this tag for questions involving vectors, quantities that have magnitude and direction.

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2 views

Finding a summarizing vector for average angle calculation

Let $L$ and $R$ be two bags of positive vectors of length $k$. Define the distance $d_{avg}$ between the bags as the average pairwise angle between the vectors. Is is possible to find a vector $l$ ...
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1answer
13 views

geometry, vectors

$\Delta ABC$ is any triangle. 1) Construct point $D$ as $\vec{CD}=\vec{CB}-2\vec{AC}$. 2) Demonstrate that $4\vec{BD}=2\vec{CA}$ 3) What can we deduce? I don't even know to construct the diagram ...
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3answers
20 views

Determine whether the vectors span $\mathbb{R}^3$

They want us to determine whether it span $\mathbb{R}^3$ and they gave us these vectors $V_1=(1,2,6), V_2=(3,4,1), V_3=(4,3,1), V_4=(3,3,1)$ and the answer is that the vectors span $\mathbb{R}^3$ . ...
1
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0answers
20 views

How to get 2nd partial derivative of a function of two vector variables

I am having trouble to calculate the expression: $$ \textbf{C}_{\textbf{q s}}\ \dot{\textbf{q}}\ \dot{\textbf{s}} = \frac{\partial^2 \textbf{C}}{\partial \textbf{q} \partial \textbf{s}}\ ...
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0answers
20 views

Transition matrix 2

$$S=\begin{pmatrix}1&4&-2\\0&-5&3\\1&6&0\end{pmatrix}$$ Find the transition matrix from $S$ to the standard basis $\{i,j,k\}$. My answer is as follows: I put $S$ in a ...
1
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0answers
18 views

two vectors division

I need to write a method (in c#) for two vectors (A = [1, 2, 3] and B = [4, 5, 6]) division. MATLAB says that A/B is 0.415584415584415, so what exactly happens during this division? how can i achieve ...
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0answers
18 views

Is the set of all points $(x,y)$ outside of an ellipse, or on the ellipse?

If $\vec{r} = \langle x,y \rangle$, $\vec{r}_{1} = \langle x_{1},y_{1} \rangle$, and $\vec{r}_{2} = \langle x_{2},y_{2} \rangle$, describe the set of all points $(x,y)$ such that ...
3
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1answer
31 views

Analogs to vectors — *unoriented* line segments

A real vector can be thought of as an oriented line segment. Linear algebra and multivariable calculus can be taken pretty far just by considering these types of objects (obviously there are ...
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1answer
19 views

How do i scale 2D vector using matrix

I know that scale matrix is 2x2 { x, 0, 0, y } basis. My vector { 100, 2 } and i want to scale it using custom 2x2 matrix. I've read that if left operand is 2D row vector, then multiplying it on a ...
0
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1answer
13 views

Finding orthogonal angles / polar coordinate of an n-dimensional vector

Orthogonal angles are the angles used when converting a vector to polar coordinates. So for vector $(1, 1)$, the orthogonal angle is $45$ degrees. Given a vector $(x_1, x_2, x_3, ..., x_n)$, what is ...
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1answer
9 views

Question involving vectors and lines

Determine the reduced equations of the line r that passes trough $A(2,-1,4)$ and $B=r_1\cap r_2$, where $r_1:\frac{x-1}{2}=\frac{y-3}{4}=\frac{z-1}{-2}$ and $r_2:\frac{x}{3}=\frac{y-1}{2}=z-2$ My ...
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0answers
28 views

Understanding notation - strange use of the del operator

I'm currently reading a paper with the following notation with the del operator which i have never encountered before: Does $\nabla _m$ just mean $\frac{\delta}{\delta \mathbf m} $ ? Furthermore, I ...
1
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0answers
11 views

I am trying to find the component of b in the direction perpendicular to a. I am trying to find an alternative route to this problem. Does this work?

c being the component of b in the direction perpendicular to a. So I used the triangular law regarding vectors. I wish I could draw a picture to make it more clear. But ill try to explain... proj ...
2
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2answers
36 views

Determine whether each of the following subsets of $\mathbb R^3$ is a subspace of $\mathbb R^3$

The following problem: Determine whether each of the following subsets of $\mathbb R^3$ is a subspace of $\mathbb R^3$ a) {(x,y,z) $\in$ $\mathbb R^3$ : x = 0} b) {(x,y,z) $\in$ $\mathbb R^3$ : x ...
0
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1answer
29 views

Divergence Theorem question2

I need to use the divergence theorem to evaluate $$\iint_S F \cdot n dS$$ when $F=y^2xi + x^2yj + z^2k$ and when S is the complete surface of the region bounded by the cylinder $x^2 + y^2 = 4$ and by ...
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votes
2answers
11 views

Parametrization of ellipse and normal vector

Parametrization of ellipse and normal vector $$F = x^2 \mathbf i + 2x\mathbf j + z^2\mathbf k \\ C: \text{ellipse} \implies 4x^2 + y^2 = 4$$ I'm trying to find the normal-vector here. I see that ...
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0answers
16 views

Find all components of the tensors $T_{ij}=u_iv_j+v_iw_j$ and $S_{ijk}=u_iv_jw_k-v_iu_jw_k+v_iw_ju_k-w_iv_ju_k+w_iu_jv_k-u_iw_jv_k$.

Given three vectors, $\vec u=(u_1,u_2,u_3)$, $\vec v=(v_1,v_2,v_3)$ and $\vec w=(w_1,w_2,w_3)$. Find all components of the tensors $T_{ij}=u_iv_j+v_iw_j$ and ...
1
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1answer
23 views

Clamp Distance Between Two Vectors

I was wondering if there is a formula to clamp distance between two Vectors. Let me elaborate. I have two Vectors, say, $V_1(x_1,y_1)$ and $V_2(x_2,y_2)$. I can find the distance '$d$' between them ...
0
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1answer
12 views

Specific arithmetical problem in matrix/vector notation (involving: norm, Cauchy-Schwartz?, triangle inequality?)

Given the following details: How is the relation below found, is Cauchy-Schwartz and the triangle inequality involved here, or something much simpler? What exactly are the steps in between?:
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0answers
7 views

Comparing paired objects in 3d space using direction angles.

I have data about paired objects in 3d space, where each object is defined by three components. What I would like to do is compare the orientations of the paired objects and see if one group of those ...
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0answers
6 views

Linear interpolation from V1 to moving V2

I am a programmer with a math problem, which I belive should be quite simple to solve - but it already consumed about 4h of my time. I just cannot figure it out. I have an object, which is located ...
0
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1answer
60 views

projectile motion with mass, find the range

a missile has the position vector P(t) = ht i + t(v − 5mt) j. where m is the mass (kg) of the missile, and h/v is the horizontal/vertical speed (respectively) the missile is launched with. Using the ...
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1answer
18 views

Length of a projected line

If a line is of true length x and is inclined in angles a,b,c with respect to the xy,yz,zx planes respectively , then how can i find the length of the projected line in the xy , yz and zx planes ...
0
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1answer
20 views

identity operator, direct sums, and projections

Let W be finite-dimensional vector space. Let $P: W\to W$ be a projection. Let U = Range(P) and V=Ker(P) (a) show that P is the identity operator on U. I dont understand the problem ...
0
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1answer
10 views

Finding end point of a segment, given start point and inclination

Consider a line segment whose start coordinates $(x,y,z)$ are known, and whose inclination $(a_1,b_1,c_1)$ in all $3$ planes is also known. The length of the line segment is known too. How do we find ...
0
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1answer
38 views

Finding a pair of Orthogonal Vectors

Want: Pair of orthogonal vectors in $R^4$ that are also orthogonal to the vector (1,1,-2,3) My attempt at a solution: I got stuck...
0
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1answer
21 views

Let W be the collection of all 2 by 2 symmetric matrices. Describe the orthogonal complement of W. (please)

A matrix is symmetric if $A^T$=A And the standard basis for symmetric matrices is [a,b], [b c] written as rows of a 2x2 matrix (sorry don't know how to make a matrix on this site). My question: How ...
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1answer
122 views

Help with finding range and equation of a position vector (projectile) [duplicate]

I'm given the position vector: $$ r(t) = ht \hat\imath + t(v − 5mt) \hat\jmath$$ where $m$ = mass, $h$ = horizontal speed and $v$ = vertical speed. Then the following data is given: ...
2
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0answers
30 views

Matrix Point-Wise Vector Multiplication

I have the following equation, where $\mathbf{M}$ denotes a singular Square Matrix (dim= $n$ x $n$), $\mathbf{x}$ and $\mathbf{y}$ denote vectors (with dimension $n$, too). The operator $\odot$ ...
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1answer
20 views

Proof regarding differentiation and vector [on hold]

Prove that rate of change of magnitude of a vector is not equal to magnitude of rate of change of vector.
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1answer
19 views

Let $M =\{ f(x)\in P_3 | \int_0^1f(x)dx = 0\}$ Find basis for M.

Let $M =\{ f(x)\in P_3 | \int_0^1f(x)dx = 0\}$ Find basis for M. solution: $P_3$ is the set of all polynomials of degree strictly less than 3, ($f(x) = a_2x^2+a_1x+a_0$). hence, $\int_0^1f(x)dx = ...
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0answers
24 views

Prove $K\cap L$ is a subspace of V, but $K\cup L$ is never a subspace.

assume K, L are proper subspaces. Prove $K\cap L$ is a subspace of V, but $K\cup L$ is never a subspace. Solution: if $v_1,v_2\in K$, then $c_1v_1+c_2v_2 \ in K$ [because K is a subspace] if ...
0
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2answers
30 views

Prove that if v is orthogonal to u, then it is orthogonal to any scalar multiple of u.

I never understand where to start with proofs, but whenever I see them done I understand them. My attempt: For this one could I just use the property of inner products to prove this? That being ...
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1answer
29 views

An inner product on $M_(2x2)$ is defind by <A,B>=trace($A^T$B). Verify that for any matrices A,B, and C in $M_(2x2)$ the following holds: [on hold]

An inner product on $M_{2 \times 2} $ is defind by =trace($A^T$B). Verify that for any matrices A,B, and C in $M_{ 2 \times 2}$ the following holds: < A+B , C > = < A , C > + < B , C >
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1answer
51 views

Finding a pair of orthogonal vectors in $R^4$

Find a pair of orthogonal vectors in $R^4$ that are also orthogonal to the vector (1,1,-2,3). What i have tried so far:
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3answers
37 views

find dimension of a vector space

Let A $\begin{pmatrix} 1 & 2 & -1\\ -2 & -4 & 2\\ 0 & 1 & 2\\ \end{pmatrix} $ . Let D = $\{B\in\mathbb{R}^{3x3}| BA = \begin{pmatrix}0 &0&0\\0 &0&0\\0 ...
0
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1answer
32 views

How do you find a basis for $\mathbb R^4$ such that it contains specific elements

How do you find a basis for $\mathbb R^4$ such that it contains specific elements: $(2,4,-1,0), (-4,-8,2,1)$
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2answers
31 views

Shortest distance between two moving points

So I ofund this question on the internet, which turned out more tricky than I thought: " The position of boat A is given by $x(t)=3-t$ and $y(t)=2t-4$ The position of boat B is $x(t)=4-3t)$ and ...
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1answer
14 views

xor-ing vectors

This question might be wrong on mathematics, but I don't know where else to put it. I have a given equation, and there is one calculation step, that I don't understand. I thought, I have to xor ...
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2answers
43 views

what does $\langle u,v\rangle$ mean?

Firstly, apologies for the very stupid question but I have forgotten what this means. I have a question I did a few months back where it says $u=(1-2i,3,2+i)$ and $v=(i,1-3i,0)$ It asks me to ...
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0answers
14 views

Intersection of curves and constructing a plane

Can someone please help me with how to approach/solve this question? Show that the following pair of curves intersect, and construct a plane that is tangent to both curves at the point of ...
1
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1answer
23 views

How should I describe this limiting operation in an equation

In the code I've written, I receive a delta between two position vectors, I then limit this delta by a maximum delta and return the value. To be clear: the direction of the vector remains the same, ...
0
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1answer
26 views

Suppose $S_1 =\{ u_1 , u_2 \}$ and $S_2 = \{ v_1 , v_2 \}$ are each independent sets of vectors in an n-dimensional vector space V.. [duplicate]

Let us assume that every vector in S_2 is a linear combination of vectors in S_1. Question: Does that mean that S_1 and S_2 are bases for the same subspace of V? I know that the answer to this ...
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2answers
46 views

Suppose $S_1 =\{ u_1 , u_2 \}$ and $S_2 = \{ v_1 , v_2 \}$ are each independent sets of vectors in an n-dimensional vector space V.

Let us assume that every vector in $S_2$ is a linear combination of vectors in $S_1$. Question: Does that mean that $S_1$ and $S_2$ are bases for the same subspace of $V$? I know that the answer to ...
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3answers
41 views

Curl of a vector field cross itself?

Is there a neat expression for $(\nabla \times f ) \times f$ for some vector field f? Here is my attempt at a solution: $((\nabla \times f ) \times f)_i = \epsilon_{ijk}(\nabla \times f )_jf_k$ $ = ...
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3answers
60 views

Determine whether the set $\{v_1 + v_2 - v_3, 2v_1 + 2v_3, -v_1 + v_2 - 3v_3\}$ is linearly dependent or independent.

We had a question on our last test that was very similar to this and I only got $2$ points of $6$ and I want to make sure I do it right this time. Here's my solution to that one: Let $v_1, v_2,$ and ...
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4answers
36 views

Let V be a vector space and W a subset of V. Suppose zero is in W and W is closed under addition. Is W a subspace of V?

I know that the answer to this question is No. My question is why is the answer no? What's missing? if possible give a specific example of both V and W such that W satisfies above conditoins but it ...
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1answer
16 views

Pendulum tension force

I realize this is physics related, although the problem is really about math so I thought it would be a good fit for this site. My illustration is supposed to depict a pendulum and the forces ...
1
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1answer
21 views

Linear Algebra Orthogonality Help

I am struggling with this one exercise from self-learning. I simply do not understand what it is asking. If someone could walk me through this problem I would be very grateful.
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4answers
72 views

Let $x$ and $y$ be real numbers such that $x^2 + y^2 = 1$. Find the maximum value of $2x - 5y$.

Let $x$ and $y$ be real numbers such that $x^2 + y^2 = 1$. Find the maximum value of $2x - 5y$. I do know how to solve this problem using trigonometry, however I need to solve it by using vectors. ...