# 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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### checking free positions to fill real entries [closed]

general vector spaces how do you check "free positions to fill real entries" in the subspace"
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### Calculate velocity vector given position on sphere, heading, and pitch

I would like to simulate a satellite's orbit iteratively using Cartesian coordinates. I am using the center of the earth for $(0, 0, 0).$ Given a heading, pitch, magnitude, and initial position, I ...
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### How is $|\Delta \bf A|$ equal to $2A \sin \frac{\Delta\theta}{2}$?

How did the equation $$|\Delta\mathbf{A}|=2A \sin \frac{\Delta\theta}{2}$$ come? Tried looking at other books too but couldn't understand. I'm not allowed to upload images directly so I'm sharing the ...
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### The dimension of vector and matrix

While I has tried to understand the principle of the dimension of diverse images (4-dimension), I has been baffled the definition of vector dimension. Everyone explaining the dimension of images said ...
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### Dot product interpretation as an area

Edit: as per the comments below, the interpretation discussed in this question only makes sense if both vectors have strictly positive coordinates. I've been looking at the dot product between two ...
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### Find the angle between the intersection of the two planes defined by $l_1=2x+y-z$ and $l_2=x+y+2z$ and the positive direction of $x$ axis .

Find the angle between the intersection of the two planes defined by $2x+y-z$ and $x+y+2z$ and the positive direction of $x$ axis . I know to find the angle between two planes we just need to find the ...
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### How is $|vector ∆A|$ equal to $2A sin ∆(theta)/2$ [closed]

How did the equation $$|\Delta\mathbf{A}|=2A sin \frac{\Delta\theta}{2}$$ come? Tried looking at other books too but couldn't understand. I'm not allowed to upload images directly so I'm sharing the ...
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### How to Find the $d^4p$ from the four vector?

Lets assume we are given the four vector of momentum P which can be written as: $$p = (p_0, p_t cos\theta , p_t sin \theta , P_L ) ........(1)$$ Where $P_L$ is the longitudinal competent. The ...
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### Crux problem #33 with vector approach

On the sides $CA$ and $CB$ of an isosceles right-angled triangle $ABC$, points $D$ and $E$ are chosen such that $|CD|=|CE|$. The perpendiculars from $D$ and $C$ on $AE$ intersect the hypotenuse $AB$ ...
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### Common perpendicular of two straight lines

I have the straight lines: $$d_1: \frac{x-1}2=\frac{y-3}1=\frac{z+2}1\\[4ex] d_2: \dfrac{x-1}1=\frac{y+2}{-4}=\frac{z-9}2$$ And I have to find the common perpendicular of these lines.
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### How to find the points of intersection of the perpendicular vector two skew lines

Correct me if im wrong, but this is what i know so far The cross product of two skew lines is the perpendicular vector between both those lines. The perpendicular vector intersecting two skew lines ...
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### Using vectors how to prove $AB=AC$? [closed]

In a triangle $ABC$, $D$ is the mid-point of the side $AB$ and $E$ is the centroid of triangle $CDA$. If $\vec{OE}\cdot\vec{CD}=0$, where $O$ is the circumcentre of triangle $ABC$, then using vectors, ...
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### Can you find a 3-D vector to a point in space from a 2-D projection?

it's my first time asking a question on Math Stack Exchange, so if I haven't provided enough details, or if there's a better place to ask such questions, please let me know. I'm using a camera on a ...
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### how do i tell if a vector is parallel to another vector in R^6?

So far in my book I haven't learned any of the parallel or perpendicular notation.. so there must be some way to tell this answer that the book hasn't told me.. I looked back and there was nothing ...
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### Bounding the length of a sequence of same-dimension vectors over a finite integer interval such that the sequence contains no weakly decreasing pair

How long can a sequence of $i$-dimensional vectors become at worst if the components of each vector are natural numbers below $m$ and the sequence contains no pair of vectors such that the later ...
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### Show for all real $u,v,w$: $\left|u+v\right|+\left|u+w\right|+\left|w+v\right|\le\left|u\right|+\left|v\right|+\left|w\right|+\left|u+v+w\right|$

Show that for all vectors $u,v,w \in \mathbb R^3$: $$\left|u+v\right|+\left|u+w\right|+\left|w+v\right|\le\left|u\right|+\left|v\right|+\left|w\right|+\left|u+v+w\right|$$ I know that we should show ...
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### Azimuth and Elevation to point from a ray with rotation [closed]

I've been wracking my head at this for a few hours now. I've been trying to find this for something I've been making for a game. Say there exists a target T within a 3D space with coordinates [xt,yt,...
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### show that the lines are all in a plane and find the equation of the plane.

Three lines $L_1,L_2,L_3$ pass through the origin with the parallel vectors $$V_1=i+2j-k$$$$V_2=3i+5j+7k$$$$V_3=2i+3j+8k$$ are given,show that the lines are all in a plane and find the equation of the ...
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### Principal Vector Exercise from Barrett O'Neill textbook

Prove that $\left|\begin{array}{ccc}{{v}_{2}}^{2}& -{v}_{1}{v}_{2}& {{v}_{1}}^{2}\\ E& F& G\\ L& M& N\end{array}\right|=0$ then $\overset{\to }{v}$ is principal vector where ...
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### What is the difference between the orientation and the direction of a vector?

I came across this recently, and was confused regarding the difference between the orientation and the direction of a vector. Does the orientation refer to the relative coordinate which the vector is ...
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### What is the difference between a point and a vector?

I understand that a vector has direction and magnitude whereas a point doesn't. However, in the course notes that I am using, it is stated that a point is the same as a vector. Also, can you do ...
I have an equation: $\vec{v}=\vec{w}\times \vec{r}$ How to I separate the $\vec{w}$ and write it in terms of $\vec{v}$ and $\vec{r}$? I tried to re-arrange this equation so that I could find the ...