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

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Construction of concurrent or parallel lines from a parallelogram (proof by vectors)

I have a problem with this probably easy exercise on vectors. Any help would be great. Let ABCD be a parallelogram. The line parallel to AB intersect BC and AD in points Q and S, respectively. The ...
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40 views

Question about forces and orthogonality

Two forces $F_1$ and $F_2$ meet at a point, the resultant is $R$ (parallelogram rule) , the measure of angle between them is $120$ degree , if the direction of $F_2$ is reversed the resultant will be ...
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2answers
38 views

How far down will the ball travel and what is the magnitude of the ball's initial vector?

Confused a little with $V_x$ and $V_y$ components and how to find the displacement of X. A football is kicked with an initial velocity of $V_x = 30 \text{ ft/sec}$, and $V_y=80 \text{ ft/sec}$ 1) ...
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3answers
22 views

mulivariable calculus-distance and planes

With 4 points A B C D, how do I find the distance from point D to the plane through A, B, C? This is a rather basic calc question I know but I'm not sure where to start. I imagine I'd probably have to ...
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2answers
24 views

linear algebra, vector transformation [on hold]

The linear transformation: $ T : \mathbb R^3 \to \mathbb R^3 $ depicting the vector $ u = (2, 3, 1) $ in $ T(u) = (4, 5, 2) $ and the vector $ v = (1, 1, 2) $ in $ T(v) = (3, -1, 2) $ find $T(1, ...
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1answer
24 views

Solving for first term in vector product

I'm trying to solve a system of equations for a physics application I've been working on, and I'm down to one thing left that's stumping me. Essentially, I need to solve $$A \times B = X$$ where $A, ...
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1answer
27 views

Why is this statement about $\text{Span}$ false?

Here is a true-false question known to be false: If $\mathbf{a}$ is in $\text{Span} \left \{ \mathbf{b}, \mathbf{c} \right \}$, then $\mathbf{b}$ is in ...
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0answers
20 views

3D Vectors and Geometry [on hold]

With the points A = (2, 0, 3), B = (1, 1, 1), C = (0, 1, −1) and D = (1, −1, 2)and using five subtractions, two cross products and one dot products find the distance from point D to the plane through ...
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0answers
21 views

General Tensor Assistance

Sorry if this is a stupid question, but it might help me grok things if I can connect from something that's intuitive to me. Consider a transformation from Cartesian coordinates to spherical ones: ...
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0answers
17 views

differentiation of log of a sum of vectors

I would very much like to be able to differentiate the following function with respect to $x$: $$ln(\sum \limits_{j=1}^{d} \theta_j \bf a_j^2)$$ Where $\bf a_j$ is a $d \times 1$ vector with $x$ in ...
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1answer
20 views

The normal plane to a path

PROBLEM: Let $\vec x(t)$ be a path with $\vec x'$x $\vec x'' \ne 0$ and suppose that there is a point $\vec x_0$ that lies on every normal plane to $\vec x$. Show that the image of $\vec x$ lies on a ...
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0answers
17 views

3D Planes and vectors question [on hold]

Points A = (2, 0, 3), B = (1, 1, 1), C = (0, 1, −1) and D = (1, −1, 2). Using five subtractions, two cross products and one dot products find the distance from point D to the plane through A, B and C. ...
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1answer
18 views

Vector equation of diagonals in rectangle

A bit stuck on part (ii) of this question: OABC is a rectangle. With respect to the origin, O, the position vectors of $\mathbf{a}$ and $\mathbf{b}$ are $2\mathbf{i} - 3\mathbf{j} + 5\mathbf{k}$ ...
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2answers
18 views

Magnitude of Average Velocity

A train travels 100 miles toward 37 degrees northwest and then 90 miles north. The whole journey takes 2 hours. What is the magnitude of the average velocity of the train?
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1answer
19 views

Computing the unit vector for a generalised helix

The space curve $$\mathbf x (t) = \begin{pmatrix} \cosh t \\ \sinh t \\ t \end{pmatrix}$$ is an example of a generalized helix, meaning that its tangent vector makes a constant angle $\theta$ with a ...
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2answers
32 views

How to prove invariance of dot-product to rotation of coordinate system

Using the definition of a dot-product as the sum of the products of the various components, how do you prove that the dot product will remain the same when the coordinate system rotates? Preferably ...
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0answers
28 views

Setting up an integral for a physics question.

The problem begins like this: a charge distribution is given by $\rho(r,\theta,\phi)=\gamma r^3cos\theta,a<r<b,0\le\theta<\pi/2$ and is zero everywhere else. The distance from the origin is ...
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0answers
16 views

Find the basis for the plane and the hyperplane

I'm studying for a midterm and this is one of the questions I am reviewing. Find the basis for the following: (a) the plane given by the equation $z-2y=0$ (b) the hyperplane $x+2y+z-w=0$ in $R^4$ ...
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1answer
45 views

What direction will the ball start to roll?

I need some help with the following question: A hill can be modeled with the equation $H=100−x^4−3y^2$, where $H$ denotes the elevation. Now a ball is placed on the hill at position ...
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0answers
23 views

Is it possible for dot product and cross product of two vectors to be zero at the same time?

Is it possible for dot product and cross product of two vectors to be zero at the same time ?
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1answer
20 views

Question about velocity vectors

Let $ \vec x(t)$ be a path of class $C^1$ that does not pass through the origin in $R^3$. If $\vec x(t_0)$ is the point on the image of $\vec x$ closest to the origin and $\vec x'(t_0) \ne 0$, show ...
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0answers
14 views

What is the direction of dot product and cross product of vector A and B? [closed]

What is the direction of the dot product and the cross product of vectors A and B?
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0answers
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vectors representation using matrix. [closed]

please any one can help with following attached questions? Thank you.
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12 views

Find the magnitude and direction angles of the resultant of the forces given.

Find the magnitude and direction angles of the resultant of forces $F_1$ and $F_2$ with initial points at the origin. $F_1$ has magnitude 50 lb, terminal point (10,5,3). $F_2$ has magnitude 80, ...
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2answers
24 views

How would I do this? Geometry with dot products [closed]

Points P = (1, 2, −1) and Q = (3, 2, 1) and the vector n = (1, 1, 3). Using a subtraction and a dot product show that Q is not on the plane through P and perpendicular to n.
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1answer
16 views

Recovering a vector from the angles it makes with the coordinate axes

I have the following problem: In order to extract features from human joint based 3D data I only consider the angles of the resulting bones (e.g., vector given by shoulder left joint to elbow left ...
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1answer
8 views

How does one obtain Hesse normal form of plane equation?

We have been studying the Hesse normal form of the plane equation, but the sketch of the plane in space given by the lecturer was horrible. Basically I ask you to explain me how does one obtain the ...
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1answer
23 views

What is the meaning of orthogonal projection of vectors?

The vector $\dfrac{x\cdot y}{y\cdot y}y$ is called the projection of $x$ along $y$. I do not understand what it means, geometrically. Can anyone give me n specific example of what it means?
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1answer
16 views

Vectors Statics and Forces

The following forces are applied to a wall bracket: $F_1 = 100N$ at $30$ degrees above the $x$-axis, $F_2= 80N$ at $20$ degrees below the $x$-axis. Find the resultant force and its direction. I have ...
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0answers
7 views

Finding the 2 point coordinates for a known edge.

Say I have an edge $A'B'$ which is a vector $(5,3, 9)$. How can I find the individual points $A'$ and $B'$ from $A'B'$? I translated the points $A$ and $B$ by a vector then combined them to make the ...
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18 views

Proving S is a subspace

Let S be a subspace of $\Bbb R ^n$ and define $S^\perp = \vec{x}\in\Bbb R^n | \vec{x}*\vec{s}=0; \forall \vec{s}\in S.$ The * means the dot product of the vector x and s. (a) Prove that $S^\perp$ is ...
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1answer
41 views

Finding a unit vector orthogonal to vectors $a$ and $b$

If I understand correctly, the cross product of vectors $a$ and $b$ is orthogonal to both $a$ and $b$. So for an assignment I have to find two unit vectors orthogonal to vector $a = \langle 1,0,4 ...
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1answer
60 views

Precalculus Vectors

Let $x$ and $y$ be real numbers such that $x^2 + y^2 = 1$. Find the maximum value of $2x - 5y$. I don't understand how to incorporate vectors into solving this problem. Or for that matter, how to ...
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1answer
46 views

Find the norm of a linear combination of vectors, given their norms

If a and b are vectors such that $\|a\| = 4$, $\|b\| = 5$, and $\|a + b\| = 7$, then find $\|2a-3b\|$. So I first squared both sides and then got $ab = -44$. What do I do now?
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8 views

How to figure out new vector direction after deflection by polar and azimuthal angles

I have a direction cosine vector in Cartesian 3D space. The vector starting point is (x0,y0,z0) and direction {i0,j0,k0}. I need to find the new direction cosine vector direction in the Cartesian 3D ...
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0answers
13 views

What are the values of components of normal of a sphere and a cylinder in polar system?

In polar coordinate system what are the values of the components of normal to the surface in terms of radius of the circle and cylinder.
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1answer
38 views

Differentiation of $xx^T$ where $x$ is a vector

How is differentiation of $xx^T$ with respect to $x$ as $2x^T$, where $x$ is a vector? $x^T $means transpose of $x$ vector.
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1answer
17 views

Minimizing a vector while keeping the same resultant force?

I had originally solved this problem using Calculus optimization. However, the teacher had a different solution available where he first tried setting $\theta$ to be $90$ degrees in order to cancel ...
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0answers
14 views

Finding plane from corners of a rectangle

I have a structure with 2 3D coordinates, each a corner of a rectangle. While they're co-linear, I also know that they will never be the adjacent corners, e.g. they always lie on the diagonal of the ...
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1answer
34 views

Probably easy vector calc question. two planes

Find the vector, or point orthogonal to plane 5x+3y+2y=0 and plane 5x+3y+2z=38 from point (0,0,0) I have been playing with things for 2 hours. update Sorry, I don't come here often. So, I had a ...
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1answer
22 views

Show that Two Vectors Making Supplementary Angles?

I just need a start. I am not looking for whole prove, but it'd be more appreciated if I get one. Q. Use Theorem u . v = |u| |v| cos a and the trigonometric identity, cos (180-a) = -cos a, to ...
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1answer
23 views

Trace of vectors

Does that sound about right? Given that x is $m\times 1$ and y is $m\times 1$ vectors, show that $ tr(\mathbf{xy'})=\mathbf{x'y}$. Attempt: By using the property of ...
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0answers
37 views

How to find the components of a vector, given magnitude and angle?

Problem The velocity of an aeroplane is $100$ km/h at an angle $30$ degree from north toward west. Draw a vector diagram to obtain its north and east components. Progress The work I already tried ...
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3answers
63 views

Circle rotating within a circle (roulette)

This was something in a course of mine I'm a bit too thick to see. If one takes a circle of radius $3$ and a circle of radius $1$, and rolls the smaller circle smoothly inside the larger one until the ...
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1answer
32 views

Vectors and polyhedra: a surprising fact

Given a $n$-faced polyhedron, associate to each face an outward-pointing normal vector with length equal to the area of that face. Show that the sum of these $n$ vectors is zero. I've already proved ...
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1answer
34 views

Physics Vector algebra question

If $\vec A=2\vec i+4\vec j-\vec k$, $\vec B=2\vec i-3\vec j+\vec k$ and $\vec C=- \vec i+3\vec j$, then unit vector in direction of $\vec A+\vec B+\vec C$. I tried to find unit vector of all vectors ...
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23 views

Calculating area

I have a triangle defined by its vectors. The triangle itself is intersected by a plane (z=0). My probpem is: I want to calculate the area of the triangle above z=0 and below z=0. I hope you ...
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2answers
27 views

Finding the scalar component of $\overrightarrow{PQ}$ in the direction of $\overrightarrow{PR}$

Context I am given the 3 points: $P(3,-1,3)$, $Q(1,-1,6)$, and $R(5,0,1)$ I know that $\overrightarrow{PQ} =(3-1)\hat{i}+((-1)-(-1))\hat{j}+(3-6)\hat{k} $ $=2\hat{i}+0\hat{j}-3\hat{k}$ and ...
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1answer
39 views

Does $\vec{a} \times \vec b=\vec a \times\vec c$ and $\vec{a} \cdot \vec b=\vec a \cdot\vec c$ imply that $\vec b = \vec c$?

Does $\vec{a} \times \vec b=\vec a \times\vec c$ and $\vec{a} \cdot \vec b= \vec a \cdot\vec c$ imply that $\vec b = \vec c$ if $\vec a \not=0$ ? My attempt- $\vec{a} \times {(\vec b- \vec c)} = 0 ...
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18 views

I need some ideas regarding working model in mathematics. The topics are conics and vectors.

Hi can someone suggest me some working mathematical models under the topics conics and vectors. It should be 12th standard level. (Higher Secondary). I am trying to help my juniors to do this project. ...