Use this tag for questions involving vectors.

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2
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1answer
16 views

Equation of plane with normal $(3,\:-4,\:6)$

Points $A$ and $B$ have coordinates $(−1,\:2,\:5)$ and $(2,\:−2,\:11)$ respectively. The plane $p$ passes through $B$ and is perpendicular to $AB$. Find an equation of $p$, giving your answer ...
-1
votes
0answers
12 views

Vector Cross-Product [on hold]

Prove that the dot product a.b=b.a for any two vectors a and b. It is really easy,but Can anyone give a sophisticated proof for this? I mean a proof which could be shown?
0
votes
1answer
16 views

Calculate forward direction vector using 2 vectors

I have 2 vectors: a(1,2,5) and b(-5,8,1) I need to calculate the forward direction vector from vector A to vector B. How do I do this? Is there a formula?
1
vote
0answers
21 views

Vector multiplication sign

In the link below there is a short excerpt from the text I'm using: I am stuck for a while on how he got that fraction result, after the dot product. I am multiplying the cross product part by $ ...
3
votes
1answer
38 views

How to mathematically determine if the magnitude of a cross product is up/down(positive/negative?)?

So, I'm a newbie at complex vector math. I'm working on a 2D physics engine, and my issue is, with angular acceleration from torque, is it supposed to be positive or negative? I understand the right ...
0
votes
0answers
15 views

What is this subspace?

Let $A_1$ be a full column rank matrix, size $n \times k_1$, with $k_1 < n$, and $A_2$ be a full column rank matrix, size $n \times k_2$, with $k_2 < n$. Let $A=[A_1, A_2]$. How does $S(A)$ ...
1
vote
2answers
63 views

How to proof equality of del dot a cross b

I am trying to prove that $\nabla \dot{}(A\times B) = B\dot{}(\nabla \times A) - A\dot{}(\nabla\times B)$ I tried expanding the RHS but the $x$ component of the vector I am getting is ...
0
votes
0answers
31 views

Rotate a Vector Towards a Point [on hold]

I was wondering, how would rotate a vector so it faces a specific point? This is in a 3d game world (where I want to rotate a character unit to face an enemy character unit). Thanks in advance EDIT: ...
0
votes
3answers
23 views

Finding a vector normal to the plane with position point and parallel to two vectors

A cross product of the two parallel vectors will get the vector normal to the plane. But I'm looking for a specific normal vector. The plane with point $A(3,2,1)$ and parallel to $u = 5i+2k$ and $v= ...
1
vote
1answer
18 views

Find the value of $a$ for which two lines are perpendicular

Two vectors are perpendicular when their dot product is zero. But how to get the dot product of two lines? $r_1= (8,-3,1)+s(12,-5,0)$ $r_2= (1,14,3)+t(5,a,b)$ The question asks for the value of ...
0
votes
1answer
30 views

Intersecting two circles using vectors

I'm trying to programmatically find the intersection points of two circles with different radii. Solving their equotations would be an option, but I thought of using vectors to do so. Assuming I ...
1
vote
2answers
31 views

Prove $\ell_{ki}\ell_{kj}=\delta_{ij}$

Prove $\ell_{ki}\ell_{kj}=\delta_{ij}$ where $\{\hat{\mathbf{e}}_i\}$ and $\{\hat{\mathbf{e}}_i'\}$ are sets of orthonormal basis vectors for $i\in\{1,2,3\}$, $\ell$'s are the direction cosines ...
0
votes
1answer
41 views

Angle between 3D vectors

I was given this problem and came up with an answer but I'm not sure I did everything right. You are on the ground standing and facing a corporate building and with a blue light at the top. $30°$ to ...
0
votes
2answers
29 views

What is the concept behind …?

Could someone kindly explain the concept behind this statement " Vector A is perpendicular to both Vector B and Vector C. So Vector A is parallel to VectorB x Vector C " Is there any rule like if a ...
2
votes
0answers
17 views

Find a point symmetrical to another point in relation to a line

Find the point Q that is symmetric to point $P(-1,-2,1)$ in relation to line $l: \frac{x}{-2}=\frac{y-3}{4}=\frac{z-4}{1}$ as well as projection P' of point P onto line l. 1) I guess we start off ...
1
vote
1answer
9 views

Find a equation of a normal vector from point A to the plane

I'm having trouble with following problem: "Find equation of normal vector from point $A(2,3,-1)$ that is normal to the plane $\pi:2x+y-4z+5=0$" It doesn't seem that tough but I can't seem to work ...
0
votes
0answers
16 views

Finding the intersection of 2 coordinates in spherical coordinate system

Sorry in advance for messing up any math term or being confusing. I have the following data: lat1, lon1, alt1, v1, h1 and ...
0
votes
1answer
61 views

Determine if one point lies between two other points on a sphere

My question is rather simple. Can I use the dot product to determine if a coordinate lies between two others? With coordinates I mean a Point P(latitude, longitude) on the surface of the sphere. I ...
1
vote
1answer
46 views

how $3i \times 3i = 9i \times i$? (i is the unit vector and $\times$ is cross product)

$i$ is the unit vector; didn't know how to write it. I'm reading a text and somewhere it uses something like $ai \times bi = (ab)i \times i$ (implicitly). I can see why this is true geometrically, ...
0
votes
2answers
74 views

Visually understanding the formula for the distance from a point to plane.

Ok, so we know that if we have an arbitrary point, $p$, and a normal perpendicular to an arbitrary plane, $n$, the distance from the point to the plane can be computed as follows: $$distance = p ...
2
votes
1answer
79 views

Why we use $\mathbb{R}^{m \times n}$ notation instead of $\mathbb{R}^{n \times m}$?

I just realised, that I use all the time the notation $\mathbb{R}^{n \times m}$, and all books and papers use $\mathbb{R}^{m \times n}$. $\mathbb{R}^{n \times m}$ is more sympathetic for me, because I ...
3
votes
2answers
64 views

Intuitive and convincing argument that functions are vectors

Back to school time again. As I'm discussing all the mathy stuff and insights gained over the summer, I cannot help but notice that many of my peers in second or third year undergrad cannot bridge the ...
1
vote
1answer
16 views

Vectors in 3 dimensions

If $a$ is a vector that makes equal angles with ${\mathbf i},{\mathbf j},{\mathbf k}$ and has magnitude $3$, then find the angle of $a$ with either of these unit vectors? Wouldn't the answer simply ...
0
votes
1answer
21 views

Vectors and co-linearity

If two vectors a and b are non-collinear, then for what values of x are the vectors $$c = (x-2)a + b$$ and $$d = (3 + 2x)a - 2b$$ collinear? No idea how to even approach the problem. I attempted ...
1
vote
1answer
22 views

Proof using vectors - trigonometric formulas

Question: If two vectors a and b make angle $\alpha$ and $\beta$ with the x-axis, prove, using vectors, that: $$\cos(\beta - \alpha) = (\cos \alpha) (\cos\beta) + (\sin\alpha) (\sin\beta)$$ I tried ...
-1
votes
1answer
29 views

Vectors as complex numbers [closed]

Generally, if vectors are simply two-dimensional, why are vectors added as complex numbers on my scientific calculator?
1
vote
1answer
19 views

Stereographic projections - equation of a plane question

The proof I'm trying to understand. I don't get why $k$ is unique. When trying to find the equation of a plane, suppose we're given a normal vector $n=(x_o,y_o,z_o)$ and a point on the plane ...
0
votes
0answers
5 views

Propagating a 3d vector to a spcific point in a 2d plane

I have an $xyz$ point $P$, and a 3d vector pointing from it denoted by $N$. I want to propagate the vector forward to a certain point in the $xy$ plane and calculate the corresponding value of $z$. ...
0
votes
2answers
35 views

How to resize a vector to a specific length?

I have a 3D vector u defined through two points A (0/2/0) and B (3/3/3). ...
2
votes
1answer
27 views

Surface of 3D Triangle

The coordinates $A(-1,0,2), B(2,-1,3)$ and $C(4,0,1)$ are the corners in the triangle $ABC$. a) Find the length of the sides in the triangle. b) Find the area of the triangle. Now I'm able to ...
1
vote
2answers
33 views

Median of a triangle.

If ${A,B,C}$ be the position vectors of the vertices A,B,C of the triangle ${ABC}$,show that the three medians concur at the point ${\frac{1}{3}( A + B + C)}$, called the centroid. Note : I don't ...
0
votes
2answers
37 views

How does a matrix change the magnitude of a vector?

I have the following problem: $z=Ax$, in which $z$ and $x$ are $N\times 1$ vectors and $A$ is a $N\times N$ matrix. I am interested in how the magnitude of $x$ changes after applies $A$ on it. Is ...
1
vote
1answer
15 views

Manipulation of Pauli Matrices

This question comes from QM but is cast as a purely mathematical question as follows: Suppose operators $\sigma_i$ satisfy $[\sigma_i,\sigma_j] = 2i\epsilon_{ijk}\sigma_k$ and (n . $\sigma)^2 = 1$ ...
1
vote
1answer
29 views

Vector cross product identity for $(a\times b)\cdot(c \times d)$

Prove that $(a\times b)\cdot(c \times d)=(a\cdot c)(b\cdot d)-(a\cdot d)(b\cdot c)$ I would appreciate some hints on how to solve this.I assume there is a method which does involve equating LHS ...
0
votes
3answers
80 views

Is this approach for testing orthogonality/parallelity of vectors wrong as I think?

In a math book four methods are written for testing parallelity/orthogonality of two vectors that are(notice $\vec v$ and $\vec w$ are approximations of vectors and we have x,y and z components of ...
0
votes
3answers
28 views

Vector Orthogonality and Length

The problem statement, all given variables and data Let $\textbf{a}$, $\textbf{b}$ be two vectors in $\mathbb{R}^n$. If $\textbf{a} + \textbf{b}$ and $\textbf{a} - \textbf{b}$ are orthogonal, then ...
0
votes
1answer
31 views

Necessary and sufficient condition for zero scalar triple product

I want to show that the vector triple product of $[x-y, b, a\times b]$, where $a$ and $b$ are not parallel is NOT equal to $0$ iff $[x-y, a, b]=0$. Attempt: As $a$ and $b$ not parallel, $a \times ...
0
votes
0answers
32 views

What does the x represent in my integral

I am working on a project in which I have to write a matlab code in order to find the effective properties of a material with a super-spherical Inclusion. In order to do this, a paper I found, by ...
0
votes
2answers
30 views

Calculating velocity of an object moving at 12m/s north, with 5m/s wind from the west

An object moving 12m/s passes north and hits an object. Due to the wind from a west direction, it is pushed sideways at 5m/s. Find the resultant velocity. I don't know where to start with this one, I ...
0
votes
1answer
43 views

testing parallelity/perpendicularity of two 3D vectors with lengths close to zero using dot product

as u know dot product and vector norm(euclidean) definitions are as following: $ \vec v . \vec w = \left\lVert \vec v \right\rVert \times \left\lVert \vec w \right\rVert \times \cos\theta = (v_x ...
2
votes
1answer
24 views

How to derive the function from its gradient?

Let $a$ be a vector and $a= \nabla\phi$ where $\phi$ is a scalar. How to find $\phi$ when $a$ is given? My approach: $a_1dx=a_2dy=a_3dz=d\phi$ So, $\phi=\int a_1dx=\int a_2dy=\int a_3dz$ but the ...
0
votes
2answers
60 views

Vectors at the same angle

Does anyone know a general way to find all the vectors at a given angle a from a vector? In two dimensions, it is one of these vectors (x,y) with parameter r. $$(- y \sin(a) + x \cos(a), x \sin(a) + ...
1
vote
2answers
16 views

Finding the basis for null space of the matrix $[0^T, 1^T]$

As part of some work I am doing, I am looking into the basis for the null space of the following matrix $$ [\mathbf{0}^T, \mathbf{1}^T], $$ where the vector of zeros is of length n and the vector of ...
1
vote
1answer
18 views

How can I find the vector between two sets of data?

I need to identify the vector between two sets of data. The goal is to correctly "guess" whether a new piece of data is in group A or ...
0
votes
0answers
28 views

translating vectors in polar coordinates to the complex plane [duplicate]

These equations model circular motion. Equation R is the position vector given in polar coordinates. What I've done is represent this vector onto the complex plane via equation (1). Equation (2) and ...
-4
votes
2answers
53 views

Orthogonalization of two Vectors [closed]

Given two vectors $v_1$ and $v_2$, which have a given angle $\theta$≠ $$\frac {π}{2}$$, in between; How would one apply a Gram Matrix to define an inner-product, in order to orthogonalize the two ...
0
votes
1answer
34 views

Difference between the norm and absolute value of a given vector.

Let's say I'm given a vector $x=(2, 3, 4)$, and the directions say to find the norm and absolute value of the vector. From what I've found, it's $\sqrt {(2^2 + 3^2 + 4^2)}$ for the absolute value. How ...
4
votes
1answer
58 views

A question in application of derivatives and vectors

Consider a skier who is sliding without friction on the hill ${y = h(x)}$ in a two dimensional world. The skier is subject to two forces. One is gravity. The other acts perpendicularly to the hill. ...
0
votes
1answer
19 views

Oblique projection for which the projection vector is at an angle of 45 degrees

dixit: A special case of oblique projection is called cavalier projection. It is given when the projection vector forms an angle of 45° with the z-axis. This means that: $$(x_p^2+y_p^2)/z_p^2=1$$ My ...
0
votes
0answers
22 views

finding best and worst matches for two vectors

I know how to find the angle between two vectors but I'm sure about part of the question I'm trying to workout where it says about give the angles that correspond to best and worst matches. when given ...