Tagged Questions

Use this tag for questions involving vectors, which are elements of vector fields.

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flux of a vector field on the surface of a sphere

enter image description here I attached a picture of the question, but basically have to find the flux of a field on the surface of a sphere. Ive tried the divergence theorem but it doesnt seem to be ...
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Dipole-Coupling Tensor: Electrostatic Dipole Moments

I've been struggling with this problem today. Here's an image of the question I'm attempting to answer. I'm relatively new to tensor algebra (I've been studying it for about a week or two), and I've ...
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How do I rotate a vector 90 degrees in a random direction?

I'm building a tree generator and I'm at the point where I want to have sub branches branch off at right angles off the current branch, in random directions. I have a 3D vector defining the direction ...
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velocity and acceleration of a disk rotating at a constant speed

A disk of radius 1 is rotating in the counterclockwise direction at a constant angular speed ω. A bug starts at the center of the disk and moves directly toward edge. The position of the bug at time ...
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How to you find out what a matrix does to an equation.

Lets say I have an equation of a plane, $$x-3y+2z=0$$ and I get matrix to transform it with say a 3x3 matrix with just a-i as place holders for the values in the matrix. How would I find what the ...
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Gram-Schmidt Process, finding orthonormal basis

Suppose I'm given $2$ random vectors $(v_1,v_2)$ I want to find orthonormal basis $(w_1,w_2)$ Are the following equivalent? for the $w_2$ case $$w_1=\frac{v_1}{\|v_1\|}$$ ...
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Cross Product of two perpendicular vectors

Say I have two perpendicular vectors $\bf a$ and $\bf b$, and any vector $\bf c$, can anything be said about $(\bf a \times \bf b) \dot \bf c$?
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What determines the direction of cross product resultant vector?

Why do we use the right hand rule to determine the direction of the vector resulting from using the cross product? A resultant vector that was directed in the opposite direction would also be ...
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How to determine if (1,0,1,1), (1,1,0,1) , (0,1,1,1) spans $R^4$?

I set up a system where $a(1,0,1,1) + b(1,1,0,1) + c(0,1,1,1) = (1,1,1,1)$ (the standard basis of R4) then i found that $a + b = 1$ $b + c = 1$ $a + b + c = 1$ which implies that $a = c = 0,$ and ...
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How to setup vector story problems

I'm studying for my trig final and I know how to do all the math, but I don't always understand how to setup the story problems. Mostly I'm struggling with vector story problems. For example: Forces ...
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Calculate a point on a line at a specific distance to other point [closed]

How I can calculate a Vector3 in a line from A to B at a specific distance of C. Or it could be a line rotated until line intersects another if they can intersect. in a 3D space, I appreciate your ...
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Vectors and tractors [closed]

Chaz is using a rope tied to his tractor to remove an old tree stump from a field. Which method given below, a or b, will result in the greatest force applied to the stump? Assume that the tractor ...
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How to find an unknown matrix which when multiplied with a vector gives the cross product of 2 vectors

Question Image I am trying to find the matrix $[u]_x$ as shown in the image. $u \times v$ is easy to calculate but how do I find the matrix $[u]_x$ such that $[u]_x v = u \times v$ ?
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Find point on rectangle where vector intercepts [closed]

I have a vector in the centre of a rectangle pointing out of the rectangle. The size of the rectangle is known. The vector is known. The magnitude of the vector is always greater than the distance to ...
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Canonical notion of parallel transport

I have a "What is the right search term?" style question: Suppose $S\subset\mathbb{R}^3$ is a surface and that we are given two points $x,y\in S$. Furthermore, take $v_x\in T_x S$ to be a tangent ...
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Primordial elements of a vector space

We were given the following problem in our Algebra class. Let $V$ be a $K$-vector space (not necessarily finite dimensional), and fix a basis $(e_i)_{i \in I}$ of $V$. If $x = \sum \xi_ie_i \in V$, ...
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Using divergence theorem to calculate surface of sphere

I want to calculate: $$\iiint_V div (\overrightarrow F \cdot \space dV)$$ with $\overrightarrow F=x^3\hat i+ y^3 \hat j+z^3\hat k$ and Surface of sphere given as $x^2+y^2+z^2=r^2$ So, first I ...
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Vectors : Line of intersection no Z axis component?

I've been doing and exposing to many vectors questions, mostly from Singapore-Cambridge A level questions, and finding line of intersection between $2$ or $3$ planes, always yield line of ...
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Finding the Gradient of a Vector Function by its Components

In Multivariable Calculus, we can easily find the gradient of a scalar function (producing a scalar field) $f : \mathbb{R^n} \to \mathbb{R}$, and the gradient function would produce a vector field. ...
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Sum of element-wise product of multiple vectors

We know $\vec{a} \cdot \vec{b} = \sum{a_i b_i}$. Is there a way to express the sum $\sum{a_i b_i c_i d_i}$ in terms of four vectors $\vec{a}, \vec{b}, \vec{c}, \vec{d}$? UPDATE: Actually I'm trying ...
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Proving that point of intersection of diagonals of trapezium lies on the line passing through the midpoint of parallel sides?

Can someone tell me the steps to solve this problem? Prove by vector method that the point of intersection of diagonals of trapezium lies on the line passing through the midpoint of parallel ...
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Maximize triple product with respect to orthogonality contraint

I have the following problem: Suppose I have a plane $p$ defined by point $\vec{q}_1$ and normal vector $\vec{n}$. Also I have a line $g_2$, defined by point $\vec{q}_2$ and direction $\vec{l}_2$ ...
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Shortest Distance between planes

This is a question which puzzled our entire math class including our teacher, I'm referring to part (b), we're fine with part (a). We don't understand the reason for taking the dot product and the ...
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Inverse kinematics - How do i compute the du?

I am at the moment trying to implement at jacobian based inverse kinematics solver, which is given a current homogeneous Transformation matrix r(q) and a desired homogenous tranformation matrix ...
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Simplify vector equation $2\mathbf c - (\mathbf a + \mathbf b)\times(\mathbf a - \mathbf b)$

The unit vectors $\mathbf a$ and $\mathbf b$ are both perpendicular to a third unit vector $\mathbf c$. Additionally, a is at an angle of $\dfrac{\pi}4$ to b. Simplify the expression: 2\mathbf c - ...
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i have posted a picture of the question . i can't do the second part and third part [closed]

enter image description herethe lines l1 and l2 have vector equations , I've shown that they intersect . i can't do the second and third part
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$O$ is a point inside cube such that $\vec{OA}+\vec{OB}+\vec{OC}+\vec{OD}=\vec{OM_1}$

Given a cube $ABCDA_1B_1C_1D_1$ with lower base $ABCD$ and upper base $A_1B_1C_1D_1$ and the lateral edges $AA_1,BB_1,CC_1,DD_1$ respectively. $M$ and $M_1$ are centres of the faces $ABCD$ and ...
I'm computing a SVD from a Matrix $m$ (columns = Documents ($D$) and rows = Terms ($T$) and truncate this matrix to lower the dimension of $m$ to $k$. From my resulting matrix $A = U \Sigma V^T$ I ...