All Questions
15
questions
1
vote
1
answer
265
views
Sum of the vectors from centre $O$ to the polygon vertices
I'm attempting to calculate the sum of the vectors from the center of a regular polygon to each of the vertices. I have already solve it in a complex analysis manner:
To represent the vertices of a ...
- 23
4
votes
1
answer
82
views
What does the difference of constants in equations of parallel straight lines mean?
I was trying to prove the formula for distance of a point in the cartesian plane from a line. And there are many easy proofs.
I was looking for something “tastier”. For equations of planes in 3d, the ...
4
votes
2
answers
340
views
If $\vec a,\vec b,\vec c$ be three vectors such that $|\vec a|=1,|\vec b|=2,|\vec c|=4$ and then find the value of $|2\vec a+3\vec b+4\vec c|$
If $\vec a,\vec b,\vec c$ be three vectors such that
$\vert \vec a\vert =1,\vert \vec b\vert =2,\vert \vec c\vert=4$
and
$\vec a \cdot \vec b+\vec b \cdot \vec c+\vec c \cdot\vec a=-10$
then find the ...
- 9,569
1
vote
1
answer
99
views
How do we know the position of fixed point in this Q?
Q: A particle moves on a given straight line with a constant speed v. At a certain time it is at a point $P$ on its straight line path. $O$ is a fixed point. Show that (OP×v)is independent of the ...
- 742
-1
votes
2
answers
415
views
Why is the direction of angle theta in circular motion towards and inwards?
Why is the direction of angle $\theta$ in circular motion towards and inwards of plane x-y axis?
I am not getting this concept at all.As the angel theta is changing ; the arc length (s in diagram ) is ...
- 742
1
vote
1
answer
712
views
Proving a Ratio With Vectors
I was playing around with vectors in Geogebra and constructed a triangle which has a cool property; this is the dude in question:
In which $AE=EC$, and $\frac{BD}{DC}=\frac{2}{3}$. ($F$ is the ...
- 424
0
votes
0
answers
25
views
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 ...
- 351
1
vote
1
answer
81
views
Finding a Vector Perpendicular to Two Other Vectors w/o Cross Products
I need to find a vector that is perpendicular to the vectors $[2, 3, 2]$ and $[4, 9, 5]$. I have not been taught the method with cross-products using matrices so I cannot use that method while solving ...
- 808
0
votes
2
answers
52
views
Understanding Linear classifiers
I'm studying about linear classifiers. We learned that points above a line satisfy $ax + b\ge 0$ and points that below the line satisfy $ax+b < 0$.
Why is it so?
More generally $\boldsymbol{w}^T\...
- 159
1
vote
1
answer
111
views
Perturbing a vector towards a line segment
Suppose I have a line segment along a unit vector $\ell$ (so $-\ell$ is equally valid) and a vector $v$.
If I want to perturb $v$ towards $\ell$, I can just add a vector $\vec{d}=\alpha(\ell-v)$ to $...
- 10.5k
3
votes
2
answers
108
views
Vectors: Why $a_1\mathbf{x}+b_1\mathbf{y}+c_1\mathbf{z}=a_2\mathbf{x}+b_2\mathbf{y}+c_2\mathbf{z}\implies a_1=b_1$ etc?
I was solving this problem earlier:
Points $X$, $Y$ and $Z$ in have the (three dimensional) coordinate vectors $\bf{x},\bf{y},\bf{z}$ respectively. Prove that the lines joining the vertices of $\...
- 371
5
votes
1
answer
755
views
Particle on vertex of a polygon moving towards adjacent particle.
Suppose we have a regular polygon with $n$ sides. On each vertex, there is a particle. Every particle moves in such a way that its velocity vector $(\vec{v})$ always points towards particle next to it....
- 7,561
0
votes
2
answers
112
views
Finding an angle between two vectors
I am trying to answer part $d)$ by using my answer to part $c)$. From what I can see, the only possible way to do this is to find the lenght of $AB$ and $OB$, and, using the angle in part $c)$, apply ...
- 75
3
votes
2
answers
1k
views
Show $ a·b = |a| × |b| \cos(\theta)$ geometrically and by using no algebraic arguments at all
I want to know if there is a more natural way of deriving $ a·b = |a| × |b| \cos(\theta)$ without using algebraic identities and looking at a figure instead. I am familiar with the algebraic method.
- 4,575
1
vote
2
answers
701
views
Angular radius of a sphere
Given a sphere with radius $r$ about a point $c$, what's the apparent angular radius $\alpha$ of that sphere from point $P$? In other words, if $\vec{o} = c - P$, what's the maximum angle another ...
- 163