All Questions
Tagged with algebra-precalculus vectors
52
questions with no upvoted or accepted answers
3
votes
0
answers
154
views
Is there a version of tuples without duplicates?
A set is a list of elements that is unordered and does not permit duplicates, so:
$$\{1,2\} = \{2,1\}$$
$$\{1,2\} = \{1,2,2\}$$
A bag or multiset is unordered, but it allows duplicates, so:
$$[1,2]=[2,...
- 447
3
votes
0
answers
53
views
How to compute similarity between users given their ratings?
I'm going to use a hypothetical Netflix as an example. Let's pretend they have 1,000,000 users and allow users to rate shows from 1 to 5 stars, and there are 500 shows total. Let's also say the users ...
- 167
3
votes
0
answers
51
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Tangent unit vectors?
The question asks to find the unit tangent vector at the specified value of the parameter. I think I know the process, but I can't for the life of me figure out why I am getting the wrong answer.
$r(...
- 23.8k
2
votes
0
answers
210
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Let $|\vec a|=|\vec b|=2$ and $|\vec c|=1$.Find the difference between maximum and minimum possible values of $|\vec a+\vec b|$
Let $|\vec a|=|\vec b|=2$ and $|\vec c|=1$. Also $(\vec a-\vec c)\cdot(\vec b-\vec c)=0$.
Find the difference between maximum and minimum possible values of $|\vec a+\vec b|$
My Attempt
$|\vec a+\vec ...
- 9,599
2
votes
0
answers
46
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Is there geometric interpretation of why $\vec{v} \cdot \vec{w}=\frac{\lVert \vec{v}+\vec{w} \rVert^2 - \lVert \vec{v}-\vec{w} \rVert^2}{4}$?
Is there an interesting geometric interpretation of the relationship
$$\vec{v} \cdot \vec{w}=\frac{\lVert \vec{v}+\vec{w} \rVert^2 - \lVert \vec{v}-\vec{w} \rVert^2}{4}$$
- 5,021
2
votes
1
answer
122
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Geometry in Vectors
Let
${A} = \begin{pmatrix} \cos \frac{2 \pi}{5} & -\sin \frac{2 \pi}{5} \\ \sin \frac{2 \pi}{5} & \cos \frac{2 \pi}{5} \end{pmatrix}$
and
${B} = \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{...
user233734
2
votes
0
answers
2k
views
finding the symmetric point
let there be $4$ points.
$A(-1,1,1), B(2,0,-1), C(1,3,-2), D(-2,-1,0)$. the $4$ points are not on the same line. the plane which goes through the points $A$ and $B$, and which is also paralel to the ...
- 3,231
1
vote
1
answer
48
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Proof that two matrices are row-equivalent iff they have the same nullspace
The matrices are both of size m x n over some field F, obviously.
The first direction of this proposition is clear enough, however the opposite direction (same nullspace -> row-equivalence) is ...
- 351
1
vote
0
answers
54
views
An exercise about vector multiplication/scalar product
I came across an exercise in vector multiplication but couldn’t find the formal answer for it to check myself.
I would really appreciate if someone could show me the correct answer for this exercise.
...
- 21
1
vote
0
answers
195
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Find a formula for the magnitude of an arbitrary linear combination ax+by |||| Find the precise condition on $a, b, c$ and $d$ under which the lin....
Let x and y be two perpendicular unit vectors.
(a) Find a formula for the magnitude of an arbitrary linear combination ax+by of x and y in terms of a and b.
(b) Find the precise condition on a,b,c and ...
- 11
1
vote
0
answers
77
views
Confusion with gradient and divergence of vector fields and scalar fields
In a proof, my teacher used the following assumption for an approximation:
$$
|\nabla n(\boldsymbol{r}, t)| \ll\left|\nabla \partial_{t} \boldsymbol{\tilde{r}}(\boldsymbol{r}, t)\right|
$$
where $n$ ...
- 853
1
vote
1
answer
300
views
Finding $k$ such that $\binom{-2}{k}$ is the direction vector of the line $y=\frac17(4x+1)$
I'm new here, I asked my friend about this question and he told me to go on this math forum. If someone can get me started on these questions it would make my day. Thank You
Find the value of $k$ ...
- 19
1
vote
0
answers
45
views
How to find the unit vector in a rhombus as a function of a unit vector?
The problem is as follows:
The figure from below shows a set of vectors. Find the unit vector of $\vec{A}+\vec{B}$ as a function of the unit vectors $\vec{u_1}$ and $\vec{u_2}$. It is known that the ...
- 4,185
1
vote
2
answers
778
views
How do I find the minimum force to be applied to a block sliding in a incline such as it moves with constant velocity?
The problem is as follows:
The figure shows a block over an incline. Find the minimum force that must be applied to the block so that the body of mass $m=2\,kg$ such as that body moves with constant ...
- 4,185
1
vote
0
answers
73
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Vectors proof: Find all planes passing through intersection of two planes
I would appreciate help on the vectors chapter of bostock and chandler core course. They give the following proof purportedly finding all planes passing through the intersection line of two ...
- 347