All Questions
Tagged with algebra-precalculus vectors
259
questions
4
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83
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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 ...
0
votes
1
answer
77
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Finding directional angle of vector in $\mathbb{R}^2$
I'm not sure if this is correct or not and need someone to check.
I have a vector $\vec{v} = 4\left(\frac{-1}{2}, 1\right) - \frac{1}{2}(4, 8)$
I simplified it to $(-4, 0)$
So the directional angle ...
- 23
0
votes
1
answer
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Projectile Vectors Speed
At time $t = 0$, a projectile of mass $m$ is launched from the origin at an angle $α$ to the
horizontal with speed $U$.
Let the position vector of the projectile be $\mathbf{r} = x\mathbf{i}+z\mathbf{...
user1071088
0
votes
1
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Recreational Math Problem about unknown amount of rotating vectors
I created this recreational math problem that where it looks like solver doesn't have enough information to solve it. This kind of algebra problem I haven't really seen in the wild before, as you don'...
4
votes
2
answers
342
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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 ...
- 9,599
1
vote
0
answers
54
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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
0
votes
2
answers
54
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Finding the equation of a parabola from its graph [closed]
can chat on discord but need help asap really struguling in this class
- 11
1
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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
0
votes
1
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41
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Prove that the addition of two unit vectors bisect the angle between the vectors themselves
Here is a picture for clarity:
So here is what I attempted:
$a \dot{} b = |a||b|\cos(\theta)$
$a \dot{} (\hat{a}+\hat{b})$ $= |a||\hat{a}+\hat{b}|\cos(\gamma)$
$a \dot{}$ $(\frac{a}{|a|} + \frac{b}...
- 1,190
1
vote
1
answer
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Problem with solving simultaneous equations
In part v of part a of the question, they asked me to find the coordinates of point P. I know that:
Also note that part v of question relates back to part iv(for context)
$|OP| = |AP| = |BP| = 5\sqrt{...
- 1,190
0
votes
0
answers
273
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Find the precise condition on a,b,c, and d under which the linear combinations ax+by and cx+dy are perpendicular.
"Let $\mathbf{x}$ and $\mathbf{y}$ be two perpendicular unit vectors.
(a) Find a formula for the magnitude of an arbitrary linear combination
$$a\mathbf{x} + b\mathbf{y}$$ of $\mathbf{x}$ and $\...
- 31
1
vote
1
answer
259
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What does being proportional mean?
Question:
Two concurrent forces act along the sides CA and CB of a triangle. Their magnitudes are proportional to $\cos (A)$ and $\cos (B)$ respectively. Prove that their resultant is proportional to $...
- 3,186
2
votes
3
answers
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I don't fully understand why Pythagorean theorem works with velocity vectors.
I get why it works with displacement because that's what the theorem was originally meant for, lengths.... I find it harder to wrap my head around it when its velocity. If anyone has a good ...
-1
votes
2
answers
78
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Why is a+b+c = a-a+c? [closed]
Why does $a+b+c = a-a+c$? I don't understand. Is it some math property that i didn't know of?
- 3
1
vote
1
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100
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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 ...
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