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

learn more… | top users | synonyms

0
votes
2answers
13 views

Parametric Representation for a Square with Side $1$ Centered at the Origin as a Function of the Angle Measured from the Positive $x$-Axis

While playing with some graphics progamming in OpenGL, I've encounterd this problem: Find the Parametric representation for a square with side $1$ centered at the origin as a function of the angle ...
-1
votes
0answers
12 views

derivative of transpose of vector w.r.t to the original vector

Hi everyone . I am trying to find d[X]^T/d[x] when x is a vector. can anybody help me?
0
votes
0answers
16 views

Solving a problem that is function of vector (norm 1)

Assume we have a vector ${\bf v}$ of complex entries and we are trying to solve for the following $$ \text{Re} ({\bf v} ^H e^{ j \text{angle} ({\bf v})})=?$$ where angle$(\bf{v}$) denotes the phasor ...
1
vote
1answer
20 views

Finding theta of two vectors provided A and B.

In class today the professor wanted to warm up our minds by reminding us of vectors. The last time I did vectors was five years ago. Moving on, the following was provided: A is a vector = 3i - 2j B ...
0
votes
3answers
28 views

Trying to show $|\overrightarrow{a}\times\overrightarrow{b}|^2=|\overrightarrow{a}|^2|\overrightarrow{b}|^2-(\overrightarrow{a}⋅\overrightarrow{b})^2$

If $\overrightarrow{a} = \langle a_1, a_2, a_3 \rangle$ and $\overrightarrow{b} = \langle b_1, b_2, b_3 \rangle$, then the cross product of $\overrightarrow{a}$ and $\overrightarrow{b}$ is the ...
0
votes
1answer
21 views

Calculus III Vectors - Projectile problem

A projectile is fired from ground level with an initial speed of $450 m/sec$ and an angle of elevation of 30 degrees. Use that the acceleration due to gravity is $9.8 m/sec^2$. The range of the ...
2
votes
2answers
21 views

Finding $P$ knowing $\overrightarrow{PQ}×\overrightarrow{b}$, $\overrightarrow{PQ}⋅\overrightarrow{c}$, $\overrightarrow{b}$, and $\overrightarrow{c}$

Let $Q$ be the point $(1,2,3)$, let $\overrightarrow{b} = \langle -1, 0, 1\rangle$, and let $\overrightarrow{c} = \langle 2, 1, 5\rangle$. It is known that $\overrightarrow{PQ} \times ...
0
votes
1answer
12 views

Find $\overrightarrow{b}$ knowing $comp_{\overrightarrow{a}}\overrightarrow{b} = 5$ and $\overrightarrow{a}$

I am trying to solve the following question: Given that $\overrightarrow{a} = \langle3, 2, -1\rangle$, find a vector $\overrightarrow{b}$ such that $comp_{\overrightarrow{a}}\overrightarrow{b} = ...
2
votes
1answer
15 views

Determining which vectors are solutions of a given system of equations.

Determine which vectors are solutions of the system. \begin{align*} & \hphantom{+}3x-2y-5z = \hphantom{+}4 \\ & \hphantom{+}2x+4y-\hphantom{1}z = \hphantom{+\llap{$0$}}2 \\ & {-}4x-8y+9z ...
0
votes
1answer
18 views

Multiplication of two exponential functions with dot product

I need to find multiplication of two exponential contain vectors as below, $$e^{i\textbf{p}.\textbf{R}_{A}}e^{-i\textbf{p}.\textbf{R}_{B}}$$ here $\textbf{p},\textbf{R}_{A},\textbf{R}_{B}$ are ...
0
votes
0answers
21 views

Parametric vector form of cartesian equation

Cartestian equation: $$-2x-y+z=6$$ I know to find the parametric vector form we can find any 3 points P, Q and R which satisfy the cartesian equation. $$ \begin{pmatrix} x_1\\ y_1\\ z_1 ...
1
vote
0answers
34 views

Simplify $e^{x \cdot \log{y}}$ where $x, y \in R^N$

I'm looking to simplify the following expression (or to determine if it's even possible). Given two vectors $x, y \in R^N$, simplify $e^{x \cdot \log{y}}$. I found it in some m-code for an infinite ...
1
vote
5answers
36 views

Seemingly impossible problem involving linear combination of vector components.

Express $\langle 4, -8 \rangle$ as a linear combination of $\vec{u}$ and $\vec{v}$, given $\vec{u}=\langle 1,1 \rangle$ and $\vec{v}=\langle -1,1 \rangle$. So, I set up: $\vec{i}=\langle 1,0 \rangle$ ...
0
votes
1answer
21 views

vector matrix division

I can multiply a vector by a matrix like so a d e f ad + be + cf b * g h i = ag + bh + ci c j k l aj + bk + al but how do I divide? ...
0
votes
0answers
11 views

Given the angles of a 3d vector and the length of one of the components find the length of the other two components

The angles of a vector are 118 with the positive x axis, 76 with the positive y axis and 148 with the positive z axis. The y direction component of the vector is 5. How do you find the other two ...
0
votes
0answers
16 views

I don't understand this definition of vector positivity in my linear algebra text

I don't understand why they say that the magnitude of v is greater than or equal to zero and then go on to say the magnitude of v is equal to zero if the vector is equal to zero. Shouldn't they use ...
1
vote
0answers
32 views

Why do we use r to represent vector-valued functions?

Many standard calculus texts use r as the default function name when defining vector-valued functions, e.g., $\textbf{r}(t)=\langle x(t),y(t),z(t)\rangle$. For scalar-valued functions, we default to ...
0
votes
1answer
18 views

Sum of the vectors from one fixed vertex to each remaining vertex of a regular polygon

I'm attempting to calculate the sum of the vectors from one fixed vertex of a regular m-sided polygon to each of the other vertices. It's for a study guide preceding my Linear Algebra exam tomorrow, ...
-1
votes
5answers
30 views

Find two vectors v1 and v2 such that when added equal (0, 4, 0).

Struggling with this question. Find two vectors $v_1$ and $v_2$ such that when added equal $(0, 4, 0)$. $v_1$ is parallel to $u(-2, 4, -2)$ and $v_2$ is perpendicular to $u$. Not sure how to start.
1
vote
1answer
22 views

Find a non-zero vector u with terminal point Q(3,0,-5) such that u is opp directed to v=(4,-2,-1)?

So for this question, this is how i approach Let's treat initial point as (a1,a2,a3) and we got the terminal point, so vector of u is (3-a) (0-b) and (-5-c) I am kind of stuck here as I as if the ...
0
votes
0answers
23 views

**Location** of shortest distance between two skew lines in 3D?

I can find the shortest distance $d$ between two skew lines $\vec{V_1}$ and $\vec{V_2}$ in 3D space with ...
0
votes
0answers
9 views

What is the perspective projection of a 3d point relative to a quarternion encoded camera?

I'm representing a camera on the cartesian space as a tuple of a 3d point (position) and a quarternion (rotation). I get the front, right and up vectors of the camera by applying the quaternion to the ...
0
votes
1answer
29 views

Find the scalar of a and b

Hi I need some help with vectors. My u is (3,1,-1,5) and v is (0,2,1,-3). Find the scalar of a and b as au + bv = (3,-3,-3,11). What i did was to add this two up, so I got a(3,1,-1,5) + b(0,2,1,-3) ...
-2
votes
1answer
37 views

Mathematics - Vectors [on hold]

There are 2 vectors $p$ and $q$. $p$ is perpendicular to $q$. $||p||=2||q||$. Find angle between the vectors ($p+q$) and ($p \times q$).
0
votes
0answers
11 views

Notation for the ith row and column of a matrix

When noting the $i^{th}$ scalar of a vector $\mathbf{x}$ one usually does it as $x_i$, since it is a scalar When doing this for matrices that are being denoted in bold, let's say $\mathbf{A}$, how ...
1
vote
1answer
22 views

Is the magnitude of the gradient non zero?

Let $f=u+iv$ be a holomorphic function on a domain $\Omega$. Suppose $x_{0}+iy_{0}=z_{0}\in\Omega$ such that $f^{\prime}(z_{0})\neq0$ and $\left\vert f(z_{0}) \right\vert > 0$. Let ...
0
votes
1answer
16 views

Assigning a specific value to components of a vector

So far, I've run into this twice and I'm not exactly sure how to make this connection myself, but in this case, I've been asked to find the dot product of $(i+j+k) \cdot (3i+2j-5k)$ I understand ...
0
votes
1answer
26 views

Is every tensor the gradient of a vector?

I guess no, since every vector is not the gradient of a scalar - I assume ! Please confirm or guide in this regard .
2
votes
2answers
30 views

Integration of a scalar function with respect to a vector

I have a scalar function that takes $n$ arguments, $f(x_1, x_2,x_n) = f(\mathbf{x})$, and two vectors also with $n$ elements, $\mathbf{z} = (z_1, z_2\cdots,, z_n)$, and $\Delta\mathbf{z} = (\Delta ...
4
votes
1answer
58 views

Let the plane V be defined by $ax + by + cz + d = 0$; with $a, b, c, d \in \mathbb{R}$ and the vector $(a; b; c)$ a unit vector.

I am battling to get my mind around some of the concepts involving vectors in $3$-space. This question asks me whether the following statements are True or False: (A) The line $(a; b; c)$ is parallel ...
3
votes
1answer
40 views

Characterization of vectors via $\ell_p$ norms

Suppose you are given all $\ell_p$ norms of a vector $v\in \mathbb R^d$. Is it true that the set of all its $\ell_p$ norms $\{\|v\|_{p},p=1,..,\infty\}$ uniquely define the vector $v$ up to ...
0
votes
1answer
26 views

Finding the equation of a line in 3D [closed]

If the line $L$ is given by the equations $2x-y-z=0$ and $x+z-1=0$, and $M$ is the point $(1,3,-2)$, how do I find the Cartesian equation of the plane: (a) Passing through $M$ and $L$; and ...
0
votes
0answers
17 views

Given a set of three-vectors, how to approximate any other vector? [closed]

The table below contains reference input points and sample output points in 3d RGB color space. Given these data, how could I arrive at a function to approximate (r_sample, g_sample, b_sample) for an ...
0
votes
1answer
11 views

Isometries and Orthogonal Matrices

I know how to show that multiplying by an orthogonal matrix preserves the angle and distance between two vectors. I have seen everywhere that Orthogonal matrices are kind of related to rotations and ...
0
votes
0answers
14 views

Derivating the normal vector from a line equation

$$g_a: \binom{x}{y}=\binom{x_g}{y_g}+\lambda\binom{a_{g_a}}{b_{g_a}}$$ $$g_b: a_{g_b}x+b_{g_b}y=c$$ Explain why: $$\vec{n_{g_a}}=\binom{a_{g_b}}{b_{g_b}}$$ Where ...
1
vote
1answer
8 views

Change of Basis in Canonical Correlation Analysis

I am studying canonical correlation analysis. And I'm completely stumped for the last few days at the following manipulation. How does the following change of basis works? The equation doesn't even ...
0
votes
0answers
25 views

Properties of vectors in $\mathbb{R}^3$ related by cross-products

If $u, v$ and $w$ are vectors in $\mathbb{R}^3$ such that $u \times w=u \times w$, which of the following will be true: a) $\pi_w u= \pi_w v$ b) $\pi_u w= \pi_v w$, where $\pi_x$ is the projection ...
0
votes
0answers
16 views

Proving that rotation-inversion axis 2 and rotation axis n/2 induce rotation axis n.

How to prove that rotation axis of n/2 order and rotation-inversion axis of 2 order induce rotation-inversion axis of n order?
0
votes
0answers
10 views

Proving that rotation-inversion axis n contains rotation axis n/2. [closed]

How to prove that rotation-inversion axis of n order contains rotation axis of n/2 order when n is even?
1
vote
2answers
65 views

What does ||u|| mean?

What does $\left\Vert \mathbf{u}\right\Vert$ mean in this equation? How would this equation be performed? I'm extremely terrible in discrete mathematics and a simplistic answer would be ideal. (Don't ...
0
votes
0answers
24 views

Find line equation if it passes through 2 points and has an angle with Oz

Line goes through point $(1,0,0)$, on z axis cuts of a, $1/√5$ long, part and with that axis has an angle of $arccos(2/3)$ I need it in this form Some questions I have about this: can I find ...
1
vote
3answers
178 views

Solving geometry problem, in a triangle, using vectors

P is the middle of the median line from vertex A, of ABC triangle. Q is the point of intersection between lines AC and BP.
-4
votes
0answers
42 views

Linear Transformations? [closed]

I have three linear transformation problems which I have no idea of how to start solving. If possible could someone guide me through this? Links to videos would be great so I can solve future problems ...
0
votes
0answers
20 views

Scaling Matrix?

I have two matrix problems which I have no idea of how to start solving. If possible could someone guide me through this? Links to videos would be great so I can solve future problems myself 1) Find ...
1
vote
2answers
17 views

Finding perpendicular vectors

Consider the following three points in $R^3$ : $P(−1, 1, 0), Q(1, 5, 6), R(3, −1, 4)$ Find the values of $x ∈ R$ for which $PR + x QR$ is perpendicular to $PR$. I was thinking that equating the dot ...
0
votes
0answers
41 views

How to solve the following vector problem

There is a parallelogram ABCD with AB on top and DC on the bottom ( see diagram image below) A point P divides AD in the ratio 1:4 with PD being the longer side A point Q divides DC in the ratio 1:4 ...
1
vote
1answer
52 views

If $\left\langle b,c\right\rangle =\left\langle c,a\right\rangle=\langle a,b\times c\rangle =\dfrac {1} {2}$, find $\left\langle a,b\right\rangle$.

Suppose $\vec {a},\vec {b},\vec {c}$ are unit vectors in $\mathbb R^3$. If $\left\langle b,c\right\rangle =\left\langle c,a\right\rangle=\left\langle a,b\times c\right\rangle=\dfrac {1} {2}$ then ...
-1
votes
0answers
12 views

Inner Product of Square Matrices

Let K$^{n*n}$ & M$^{n*n}$ be two square matrices, and K$\cdot$M= \begin{matrix} t_{11} & \cdots & t_{1n} \\ \vdots & \ddots & \vdots \\ t_{n1} & \cdots ...
0
votes
4answers
26 views

Proof for parallelogram law of vector addition

The Statement of Parallelogram law of vector addition is,If two vectors are considered to be the adjacent sides of a Parallelogram, then the resultant of two vectors is given by the vector which is a ...
0
votes
0answers
13 views

Dot Product of Square Matrices & Inner Product

I need some help! Thank you in advance. Let K$^{n*n}$ & M$^{n*n}$ be two square matrices, and K$\cdot$M= \begin{matrix} t_{11} & \cdots & t_{1n} \\ \vdots & \ddots ...