All Questions
Tagged with algebra-precalculus vectors
258
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
0
votes
0
answers
24
views
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} \\
...
- 11
0
votes
0
answers
28
views
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 ...
- 111
1
vote
1
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48
views
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
-2
votes
2
answers
97
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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 ...
- 59
5
votes
7
answers
289
views
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 ...
- 81
2
votes
1
answer
130
views
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 ...
- 21
3
votes
1
answer
132
views
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
2
votes
0
answers
209
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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 ...
- 9,569
-2
votes
1
answer
50
views
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?
1
vote
1
answer
74
views
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
votes
1
answer
92
views
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 $\...
- 164
0
votes
1
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49
views
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 $p_1$, $p_2$...
0
votes
1
answer
33
views
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
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 ...
