All Questions
Tagged with algebra-precalculus vectors
259
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I don't understand how difference of vectors work {HOMEWORK} [duplicate]
So in the picture we have vectors u and v. Our goal is to find $v−u$
From what I know, the subtraction of vectors is just reversing the direction of the $2^{nd}$ vector & then finding the ...
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1
vote
1
answer
270
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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
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How do I prove that the angle between two 2d vectors depends of sign of dot product of two 2D.?
How would you prove that given two 2D vectors in the $\vec{v} = \begin{bmatrix}
v_{1} \\
v_{2} \\
\end{bmatrix}$ and $\vec{u} = \begin{bmatrix}
u_{1} \\
...
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28
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Determination of a positive basis
In 1-4 of Do Carmo's Curves and Surfaces, he states that so long as $\mathbf{u} \land \mathbf{v} \neq 0$ for two vectors $\mathbf{u}$ and $\mathbf{v}$ (where $\land$ denotes the cross product between ...
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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 ...
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2
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Advanced Algebra Problem Maybe linked with Vectors? [duplicate]
$x^2 +y^2 + xy = 25$
$y^2 + z^2 + yz = 49$
$z^2 + x^2 + zx = 64$
Find $(x + y + z)^2 -100$
Here's My Approach :
$x^2 + y^2 -2xycos120 = 25$. This Equation looked too similar to the subtraction of the ...
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votes
7
answers
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Why is $x_1 x_2 + x_1 x_3 + x_2 x_3$ constant for an equilateral triangle?
Consider an equilateral triangle centered at the origin of the 2D Cartesian space. Let the coordinates of its vertices be $v_1=(x_1,y_1)$, $v_2=(x_2,y_2)$ and $v_3=(x_3,y_3)$. All such triangles can ...
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votes
1
answer
131
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Do the BEDMAS rules apply to different types of mathematical objects, such as matrices or vectors?
I know that the BEDMAS rules (Brackets - Exponents - Division OR Multiplications - Addition OR Subtraction) for Order of Operations apply to scalars and algebraic expressions.
Do the BEDMAS rules for ...
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votes
1
answer
133
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Equation of plane $\mathbf{x} = (1, 0, 1) + s(1, 3, -1) + t(2, 2, 1)$
I'm given that the plane $W$ in $\mathbb R^3$ can be written as
$$W: \mathbf{x} = (1, 0, 1) + s(1, 3, -1) + t(2, 2, 1)$$
where $s$ and $t$ are real numbers.
My task is to write $W$ as a general ...
- 39
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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
1
answer
50
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Why can the dot product of two vectors be written in the form $a_x b_x + a_y b_y + a_z b_z$ [closed]
My intuition says that $(a_x + a_y +a_z) \cdot (b_x + b_y + b_z) $ would expand out to be a quadratic... Why isn't this the case?
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1
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How is this equation valid$?$
If $$\vec a×\vec r=\vec b+t\vec a$$ and $$\vec a \cdot\vec r =3$$ where $\vec a =2\hat i+\hat j-\hat k$ and $\vec b=-\hat i-2\hat j+\hat k$ then find $\vec r$.
I have found the $\vec r$.
My question ...
2
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1
answer
95
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Using vectors, find the rate of change of distance between two particles.
Particle A moves along the positive x-axis, and particle B along the line $$y=-\sqrt{3}x$$ for $x\in\left(-\infty,0\right]$ where $x$ and $y$ are in meters. At a certain time, $A$ is at the point $\...
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49
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Determining the centers of two circles at the moment of contact
This problem appeared in a coding project im in the middle of and its driving me crazy. The problem is as follows:
Assume there are two circles $c_1$ and $c_2$, with known position vectors $p_1$, $p_2$...
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votes
1
answer
34
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Average angular velocity of a particle that retrogrades based on position of another
I originally thought that this problem would be trivial to solve, but it has proven more difficult than I expected.
Suppose there are two runners on a circular track with radius r. Runner a runs at a ...
4
votes
1
answer
83
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 ...
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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 ...
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71
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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
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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'...
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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 ...
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vote
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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.
...
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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
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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 ...
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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}...
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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{...
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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 $\...
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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 $...
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3
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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 ...
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2
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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?
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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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