# Questions tagged [vectors]

Use this tag for questions and problems involving vectors, e.g., in an Euclidean plane or space. More abstract questions, might better be tagged vector-spaces, linear-algebra, etc.

7,493 questions
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### Elementwise Matrix Derivative

In the context of a neural network, where $l=1,...,N$ denotes a layer, I have a linear mapping: $$\tilde{x}^{(l)}:= W^{(l)} x^{(l-1)} + b^{(l)}$$ where $x$ a vector with input, $W$ a matrix ...
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### Prove that $u\cdot v = \frac{1}{4}||u+v||^2 - \frac{1}{4}||u-v||^2 \forall u,v \in \mathbb{R^n}$

I am trying to prove the above statement but I'm not sure if my proof is correct. My proof is as follows, Given $u\cdot v$, we know by the C-E Inequality that $|u \cdot v| \leq ||u|| \ ||v||$ ...
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### Intersection of the two planes

I need help with my vector's assignment!!! Let L be the line of intersection of the two planes x+y+z-1=0 and 2x+3y-z+2=0. Find the scalar equation of the plane that contains the line L and passes ...
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### Intersection of a plane

I need help with my grade 12 Vector's homework. Can a plane be perpendicular to the x-axis and contain the line $x=z, y=0$? Explain. I really hope someone can answer this question
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### Find the equation of the plane that passes through the line of intersection of two planes and a point

Find the equation of the plane that passes through the line of intersection of the planes $2x-3y-z +1 =0$ and $3x+5y-4z+2=0$, and that also passes through the point $(3,-1,2)$ $\vec n_1 = [2,-3,-1]$ ...
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### collision point of circle and line

I'm trying to figure out the collision point of the circle and a line, ultimately it should work in 3D but for now just in 2D to simplify the problem as much as possible. I've created 2 examples here ...
0answers
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### Erroneous vector filtering from image [on hold]

I am working on the motion estimates using two images by python based algorithm. I got the attached vector field (green color). This field includes some erroneous vector. I want to filter those ...
1answer
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### How to calculate the vector intersecting a sphere tangent and plane

I have a sphere centred at a point (x, y, z) = (0, 0, 0) with radius r = 1. I have a point P on the outside of the sphere. How could I calculate a vector at P, which points along both the tangent ...
1answer
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### Given: $u, v \in \mathbb{R}^3$ find all vectors $w$ such that $u \cdot v = w \cdot u$ [on hold]

I have the following problem, but I do not know how to approach it. Given: $u, v \in \mathbb{R}^3$ find all vectors $w$ such that $u \cdot v = w \cdot u$ (dot product) Can anyone give me a hint on ...
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### why any vector can be wriiten as the sum of two components in the row space and nullspace?

My textbook says that: there is a $m\times n$ matrix A, any vector x in $R^n$ can be written as the sum of a component $x_r$, in the row space, and a component $x_n$ in the nullspace: $$x=x_r+x_n$$ ...
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### Area of parallelogram 3D vectors

I'm given the following parametrization of a parallelogram $(x,y,z)=(1,1,1)+s\cdot(2,-1,-1)+t\cdot(-1,3,2),s\in[0,1],t\in[0,1]$ I'm now asked to determine the area of this parallelogram as well the ...
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### Finding two unknown scalars using vectors GCSE

Asking about question 9d) in attached photo. I have the mark scheme to this question (also attached) and I understand the principle of 9d). I think you have to equate it somehow, using the ...
1answer
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### Linear dependence of three vectors

Could someone please explain why, if two vectors in a set of three are parallel to each other, that this implies that the whole set of three vectors is linearly dependent? I have tried to show this ...
2answers
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### Why is the dot product the projection of one vector onto another? [closed]

Could you please give me an intuitive explanation why the dot product is defined this way?
1answer
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### If $B$ is added to $A$, under what condition does the resultant vector have a magnitude equal to $A+B$?

If $B$ is added to $A$, under what condition does the resultant vector have a magnitude equal to $A+B$? Under what conditions is the resultant vector equal to zero? My Attempt: Let $\theta$ be the ...
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### Vectorial and parametric equation

I was solving some vectors exercises but I came across with some doubts about them. I don't know how to do this exercise, so I would appreciate some help. Thanks. 1) Find a parametric and a vectorial ...