# 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.

7,400 questions
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### Coplanar points and vectors pointing them from 0xyz axis

Let 4 points be A,B,C,D and vectors starting from(0,0,0) in xyz axis a,b,c,d accordingly(for example the vector 0A is a) If the 4 points A,B,C,D are coplanar then proof [(a,b,c) is the scalar triple ...
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### Linear algebra identity evaluation

I really couldn't find anything related to this simple identity I came up with so: $$\vec{r}=(r_x,r_y)=(r_x, \angle0)+(r_y,\angle\frac{\pi}{2})$$ My thinking process was that $r_y$ is practically ...
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### what is the result type 3D vector, point and scalar arithmetic operations?

I doing programming but I am not good at math. I want to represent point and vector in different type. Both point and vector are tuple of 3 elements, where point represent location and vector ...
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### Find a function M

Let $x(t)$ be a real valued vector. Can you find a function M such that $\dot{M}=\frac{\text{d}M}{\text{d}t}=\dot{x}^T\dot{x}$. I have tried $M=\dot{x}^Tx, M=x^Tx$ and many more which don't work. ...
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### Arrangements of terms in the dot and cross products [on hold]

Why is the arrangement of terms in the cross product important and not important in the dot product
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### Average direction between two vectors

this is my first time asking a question so I'm sorry in advance for any mistake I might make. So I have 3 points in 3D space: A, B and C. What I want to do is have an object on point B point towards ...
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### Serge Lang (introduction to linear algebra)

I am reading Introduction to linear algebra by Serge Lang. I have a confusion. I read here on website that we cannot add points. But he defines this operation. how can this be?
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### Orientation(arrangement) of the terms of a cross product or dot product

when taking the cross product of 2 vectors, why is their arrangement important, and not important when taking their dot product? (why is Ā×Ū=-Ū×Ā in the cross product, but Ā×Ū= Ā×Ū in the dot product)
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### Introduction to linear algebra (Strang) 1.1 problem 20

Under what restrictions on c, d, e, will the combinations c$u$+d$v$+e$w$ fill the dashed triangle? ($u$, $v$, $w$ are 3-d vectors) I have been trying to see the way I could make restrictions on c, d ...
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### vectors equation of a plane [on hold]

Does the line with equation (x, y, z) = (5, -4, 6) + u(1,4,-1) lie in the plane with equation (x, y, z) = (3, 0, 2) + s(1,1,-1) + t(2, -1, 1)? Justify your answer algebraically.
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### Vector Equation of a plane

The lines $L1$ and $L2$ have equations $r = 8i - 14j + 13k + s (-4i + 7j - 6k)$ and $x/2 = (y-17)/5 = (z+7)/-1$ respectively. The plane contains both $L1$ and $L2$: a) Find the vector equation of the ...
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### Vectors and line equations and planes

Which of the three coordinate planes does the line given by $x=16t, y=-4-9t, z=34$ intersect? I am confused where to start with this question. I was thinking maybe to solve $t$ from equation of $y$ ...
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### Mistake in calculations related to vectors and norms

I am rather new to calculus, and am trying to resolve the following question. I have come to an answer, but it is not listed amongst the possible answers, so I would love to know where my reasoning ...
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### Real valued vector representation of Hermitian matrix

Since my application is in physics, I created a specialized version of this question on physics.SE. One can write a symmetric matrix $M \in \{\mathbb{R}, \mathbb{C}\}^{n \times n}$ in a half-...
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### Linear Algebra question. Finding vector component of $\bf u$ orthogonal to $\bf a$ [on hold]

Let $\mathbf u = (2, 1, -1),\mathbf a = (-3, 2, -1)$. Find the vector component of $\bf u$ orthogonal to $\bf a$. I followed a solution I found on the internet but the system keeps saying half of the ...
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### Degree between vector and point

I have a vector and a point $(x, y)$. The vector starts from $(0, 0)$ and goes to $(x_1, y_1)$. $x$, $y$, $x_1$, $y_1$ are known. How can I get the degree that vector should rotate clockwise to face ...
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### Find the vector projection and component perpendicular

Question: If vector $a = <2,3,5>$ and vector $b = <2,-2,-1>$, find the vector projection of b onto a and hence find the component of b perpendicular to a. I found the vector projection of ...
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### Prove $(X \theta - \vec{y})^T (X \theta - \vec{y}) = \theta^T X^T X \theta - \theta^T X^T \vec{y} - \vec{y}^T X \theta + \vec{y}^T \vec{y}$

I'm studying Machine Learning Stanford's CS229 course and in the lecture note, page number 11, I'm not getting how does step 2 arrive from step 1 above? Prof. Andrew Ng says that it is the expansion ...
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### $\mathbb{E}[\operatorname{sign}\langle v,z\rangle]$ for $v$ fixed, $z_i\sim N(0,1)$

I am trying to evaluate $\mathbb{E}[\operatorname{sign}\langle v,z\rangle]$ for $v\in\mathbb{R}^n$ fixed and $z_i\sim N(0,1)\ \forall\ i\in[n]$. The $\operatorname{sign}$ part is what is confusing ...
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### Is this possible in vector calculus?

$$(\boldsymbol{\nabla}\alpha)\wedge(\boldsymbol{\nabla} \wedge \boldsymbol{x} )$$ In all the examples in lecture, it has always been a $$\boldsymbol{\nabla}$$ on the left hand side. Does this give ...
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### How to fiind the relationship between a given plane equation and a line equation?

Given some plane equation P $x-3y+2y = 4$, and line l $r(t) = <4t, 2t, 2+t>$, how do I find their relationship? For example, are they orthogonal? Parallel? Is l contained in P? I would ...
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### Question about vectors and geometry in calculus

I am rather new to calculus, and was asked to answer the following question. I think I have the right answer, but I would love some feedback, particularly because some answers I derived empirically, ...
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### Velocities calculation in X Y Z directions for GNSS from Speed [closed]

The Speed and location coordinates at each GNSS location are given. How can be the velocities along X, Y & Z directions at each individual GNSS location calculated ?
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### Understand reflections in the plane

A plane is spanned by the vectors $\vec{a}$ and $\vec{b}$. The angle between the mirror axes $\vec{a^\perp}$ and $\vec{b^\perp}$ is equal to the angle of the two vectors $\vec{a}$ and $\vec{b}$. Let'...
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### Does the line passing through $(3,4,-1)$ which is normal to $x+4y-z = -2$, intersect any of the coordinate axes? [closed]

Does the line passing through $(3,4,-1)$ which is normal to $x+4y-z = -2$, intersect any of the coordinate axes? I'm not sure how to go about this question. Any help would be greatly appreciated. ...
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### What is the meaning of angle between two planes?

Suppose there are two planes that have normal vectors n1 and n2. Let vector n2' = -n2. So, n2' is also the normal vector of plane 2. We can see that the angle between n1 and n2, and between n1 and n2' ...
I have the field: $$\bar a(\bar r)=r \bar c + \frac{(\bar c\cdot \bar r)}{r}\bar r$$ where $$\bar c$$ is a constant vector. I have worked through the problem and I cant seem to easily show that:  \...