# 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.

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### Is there an elegant method to separate a 2-dimensional vector into a diagonal vector and a vector following either the x or y axis?

Hello dear Mathematics users, Is there an elegant method for separating a vector into two vectors, one diagonal and the other collinear to either the x or the y axis, so that the sum of their ...
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### Expressing polynomial equations as a set of linear equations

Suppose the $4$-vector $c$ gives the coefficients of a cubic polynomial $p(x) = c_1 + c_2x+c_3c^2+c_4c^3$. Express the conditions $p(1) = p(2), p'(1) = p'(2)$ as a set of linear equations of the ...
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### Integrating unitary vector in calculating stress resultant

The problem defines: velocity in the local base $\{e_r , e_\theta , e_z\}$, the gradient and acceleration in the local curvilignear base $e_{i} \otimes e_{j}$ avec $i, j \in\{r, \theta, z\}$ ...
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### Planet Zog: Gravity of a Sphere with Spherical Deletions

Years ago I was given this problem to do. I couldn't manage it at the time but was given the broad strokes of the solution. I came across it again recently and decided to have a go. Could someone ...
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### Axial vector of a skew symmetric tensor

What is the relationship between the magnitude of axial vector and the magnitude of its corresponding skew tensor? How can we derive it?
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### The exact value of the norm of two vectors

I'm able to find the minimum and maximum values for the norm of the sum of two vectors using the triangle inequality, but I'm not sure if I can find the exact value without knowing the angle between ...
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### Can a flux that varies only in $x$ through surface $ds$ be separated into $dx$ and $dy$ terms

For a vector such as this, if $ds$ was vertical, it could be written as $F(x)dy$. However, as $ds$ varies with $x$, can it be written as a with respect to only $F(x)$, $dx$ and $dy$ terms? The general ...
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### Angle between these two vectors

A mapping tool moves from point $a$ {199,176} to point $b$ {199,164} then moves to point $c$ {198, 185} the movement coordinates in the image shows this. the question is what is the angle that ...
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### $\pi-2\pi$ angle between two 3D vectors

I need to calculate the angle between two 3D vectors. There are plenty of examples available of how to do that but the result is always in the range $0-\pi$. I need a result in the range $\pi-2\pi$. ...
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### Make two vectors equal to each other.

Consider you have a array $a=[x_1,x_2,x_3]$ and array $b=[y_1,y_2,y_3]$ and i need to convert $a$ to to $b$ using minimum number of operations. Valid operations are Choose a integer $k$ (by integer ...
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### Diagram shows quadrilateral ABCD, with OA = (-6,3) , OB = (5,5), OC = (7,-2) , OD = (-4,-6). Show that midpoints P, Q, R & S form a parallelogram.

The diagram below shows the quadrilateral ABCD, with OA = (-6,3) , OB = (5,5), OC = (7,-2) , OD = (-4,-6). Show that the midpoints P, Q, R & S form a parallelogram. My working out so far: ...
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### Why is the derivative of the binormal vector parallel to the normal vector?

In my notes, it says to consider an arc length parameterization r(s). Then we can show that B' points in the direction of N such that we can write B'=-𝜏N. I understand why ||B'||=𝜏 but am unsure how ...
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### How to solve $k_b \bar b - k_a \bar a + \frac{1}{t} \cdot k_a \bar a - \frac{1}{t}(\bar c - \bar a_1) = \bar a_1 - \bar b_1$

I need to solve $k_b$, $k_a$ and $t$ in this equation in a program I'm creating: $$k_b \bar b - k_a \bar a + \frac{1}{t} \cdot k_a \bar a - \frac{1}{t}(\bar c - \bar a_1) = \bar a_1 - \bar b_1$$ All ...
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### How to find linearly independent vectors?

There are three vectors: $$a_1 = (-1, 1, 0, x)\\ a_2 = (2, -3, 1, 2)\\ a_3 = (1, -2, 1, -1)$$ How can I find the parameter x so that these vectors are linearly independent? I'm not quite sure how to ...
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### Prove by using vectors $(\vec {AP} +\vec {CP}+\vec {BP})=\vec 0$ [closed]

Let A,B,C be the points of triangle and P inside of triangle. How can I prove using vectors that: $$(\vec {AP} +\vec {CP}+\vec {BP})=\vec 0$$ only if P is centroid
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### Applying span twice to a set of vectors

Consider a line $\ell$ in $\mathbb R^2$ that passes through the origin. What happens when one applies span twice? Particularly, what is $\operatorname{span} \{\operatorname{span} \{\ell \} \}?$
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If an orthogonal coordinate system transforms to another system of coordinates which is not orthogonal, then does the relation between the direction cosines in the orthogonal system, i.e. $l^2+m^2+n^... 1answer 33 views ### How are velocity vectors calculated when speed and change vector is given? This is related on an insanely hard geometry problem on Codeforces that I am struggling with: RC Kaboom Show The jist of the problem is as follows: Given an infinite 2D field, you can place$n$... 1answer 23 views ### Condition for collinearity of points? Under which of the following conditions will the points$A, B, C$with position vectors$\vec a$,$\vec b$and$\vec c$respectively be collinear? (a)$\vec c-\vec a = 2(\vec b-\vec a)$(b)$|\vec ...
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We have three points labeled 1, 2 and 3 and an angle in the following image. It is easy to show that the gradient of $\theta$ with respect to the position of the point 1 (i.e. when the other two ...
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### What is the intuition behind a Frobenius norm?

I am reading up on how to find the closest correlation matrix and they approach it by minimizing a weighted Frobenius norm. Now I am trying to understand the intuition as to why they use this. Let's ...
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### Find a vector from this equation

I have a directional vector $L_d$, that is the last direction that something has been moved. This vector is normalized. I also have the target point $T$ of this directional vector. The problem is, ...
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