All Questions
Tagged with algebra-precalculus vectors
259
questions
1
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35
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Equation of movement
The equation of movement of a certain particle on the plane XY is given by the equation:
$\vec{r}=4\cos(3t)\hat{i}+4\sin(3t)\hat{j}$ m, where t is in seconds.
Prove that the trajectory of the particle ...
- 77
1
vote
1
answer
716
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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
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votes
2
answers
285
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Express each of the vectors in terms of i, j, and k when k is not parallel to any of the sides (and the figure is tilted)
In the following question, I am absolutely unsure of how to find vectors $AM$ and $GM$.
I know that, to find a vector, $AM$ would equal $OM - OA$.
(I think) my issue is that the direction $k$ is not ...
- 15
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3
answers
78
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Prove that if the sum of $\vec{a}$ and $\vec{b}$ and the difference of vectors $\vec{a}$ and $\vec{b}$ are perpendicular
Here's the full problem:
Prove that if the sum of $\vec{a}$ and $\vec{b}$ and the difference of vectors $\vec{a}$ and $\vec{b}$ are perpendicular, then the magnitude of $\vec{a}$ and $\vec{b}$ must be ...
- 77
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4
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209
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Linear algebra: proving these vectors form a basis of $\mathbb{R}^{4}.$
Given $v_1 = (1, 0, 1, 2)^T$, $v_2 = (0, 1, 1, 0)^T$, $v_3 = (−1, 2,
1, 0)^T$, $v_4 = (0, 0, 1, 0)^T$.
Prove that $v_1, v_2, v_3, v_4$ form a basis of $\Bbb R^4$.
I have no idea because I thought ...
- 37
1
vote
2
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350
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finding the theoretical speed based on current speed
A bird is attempting to fly northeast at a constant speed, but a wind blowing southward at 5 miles per hour blows the bird off course. If the bird’s overall movement (incorporating its intended ...
3
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0
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154
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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
0
votes
0
answers
14
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Vector operation that would result in unique vector outcomes by preserving the order of appearance of the input vectors
What could be a (good) mathematical operation/function that would take a certain number of $n$-dim vectors and always outputs a unique $m$-dim vector, the uniqueness of which also depends up on the ...
- 101
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1
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112
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Determining Acceleration to Intercept Accelerating Object
I'm trying to determine direction in which a missile should accelerate to hit a target in a 3D space simulation. The position and velocity of the missile, as well as the position, velocity, and ...
- 111
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1
answer
4k
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Finding the point of intersection with vectors
I'm trying to solve the following problem to no avail:
Let $𝐫_1(𝑡)=⟨8,−5,1⟩+𝑡⟨0,−1,−4⟩$ and $𝐫_2(𝑠)=⟨12,−3,5⟩+𝑠⟨1,0,−1$⟩. Find the point of intersection, $𝑃$, of the two lines $𝐫_1$ ...
- 911
1
vote
2
answers
287
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How to find elapsed time for two trains to cross each other when they travel in the same direction?
The problem is as follows:
Two trains which have different lengths each are going to meet by
traveling on different tracks with speeds $v_{1}$ and $v_{2}$
respectively. They take $20\,s$ to cross ...
- 4,185
0
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1
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42
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How to make a 2-d linear function using a third variable for the iterator? [closed]
Say, for example, you have the vector $\vec {PQ} = \langle8,4\rangle$. As we all learned in Algebra I, the "traditional" slope (y-units per x-unit) would be $\frac{4}{8}$, and the slope for ...
- 163
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43
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Numbering of indices, is $\mathbf b=(b_0, b_1, \dots, b_{n-1})$ a tuple of $n-1$ components?
I have a couple of questions regarding the numbering of indices for vectors.
For a the vector
$
\mathbf a=(a_1, a_2, \dots, a_n)
$,
I know this is a tuple of $n$ components.
But if I have
$$
\mathbf ...
- 451
3
votes
1
answer
711
views
Matrix-vector multiplication/cross product problem
How can I generally solve equations of the form $\mathbf{A} \mathbf{w} =
\begin{pmatrix} x \\ y \\ z \end{pmatrix}
\times \mathbf{w}$ for the matrix $\mathbf{A},$ where $\mathbf{w}$ can be any vector? ...
- 47
0
votes
2
answers
79
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How to find the acceleration of a cart sliding over a wire?
The problem is as follows:
The diagram from below shows a cart has a mass of $2\,kg$ is carrying
a solution of sucrose as ballast which has a mass of $6\,kg$. Below
the cart there is a brass sphere ...
- 4,185