All Questions
Tagged with algebra-precalculus vectors
18
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Proof with 3D vectors
Let ${a} = \begin{pmatrix}x_a\\y_a\\z_a\end{pmatrix}$, ${b} = \begin{pmatrix}x_b\\y_b\\z_b\end{pmatrix}$, and ${c} = \begin{pmatrix}x_c\\y_c\\z_c\end{pmatrix}$.
Show that $(x_a,y_a,z_a)$, $(x_b,y_b,...
user233734
5
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1
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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....
- 7,551
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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
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Vector Applications in Euclidean Geometry
Pentagon $ABCDE$ is inscribed in a circle. For any edge of $ABCDE$, we can draw the line perpendicular to that edge that contains the centroid of the remaining three vertices. Show that these 5 lines ...
- 61
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projectile motion with mass, find the range
a missile has the position vector P(t) = ht i + t(v − 5mt) j. where m is the mass (kg) of the missile, and h/v is the horizontal/vertical speed (respectively) the missile is launched with.
Using the ...
- 97
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Airplane ground speed and direction, given airspeed and wind
An airplane heads northeast at an airspeed of 900 km/hr, but there is a wind blowing from the west at 60 km/hr. In what direction does the plane end up flying? (angle). What is its speed relative to ...
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If $a=\langle12,5\rangle$ and $b=\langle6,8\rangle$, give orthogonal vectors $u_1$ and $u_2$ that $u_1$ lies on a and $u_1+u_2=b$
Question
If $a=\langle12,5\rangle$ and $b=\langle6,8\rangle$, give orthogonal vectors $u_1$ and $u_2$ that $u_1$ lies on a and $u_1+u_2=b$
My steps:
I am not sure whether or not $u_1$ has to lie in ...
- 2,685
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4
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Vectors and Norms
If $a$ and $b$ are vectors such that $\|a\| = 4$, $\|{b}\| = 5$, and $\|{a} + {b}\| = 7$, then find $\|2 {a} - 3 {b}\|$.
I couldn't figure out how to start off this problem. I attempted to use $$\cos ...
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Why no slope for a plane?
Similar to how lines have slopes defined in terms of $\Delta y$ and $\Delta x$, why can't planes have slopes defined in therms of $\Delta x$, $\Delta y$, and $\Delta z$?
Couldn't these could be ...
- 4,198
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Why does $\vec{V_1}\times\vec{V_2}\cdot \overrightarrow{M_1M_2}\neq0$ imply that the two lines with $V_1$ and $V_2$ as direction vectors are skew?
How come that when we want to prove that two lines are skew (that is that they don't intersect nor that they are parallel) we show that $C:=\vec{V_{1}} \times \vec{V_{2}} \cdot \overrightarrow{M_{1}M_{...
- 3,231
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Geometry in Vectors
Let
${A} = \begin{pmatrix} \cos \frac{2 \pi}{5} & -\sin \frac{2 \pi}{5} \\ \sin \frac{2 \pi}{5} & \cos \frac{2 \pi}{5} \end{pmatrix}$
and
${B} = \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{...
user233734
1
vote
1
answer
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How to properly use random projection to significantly reduce the dimensions of a vector?
In my application, I have a vectors of arbitrary length, but that normally fall in the range of between 0 and 500 elements. Each value in the vector is between -1 ...
- 167
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Solving vector equation employing products.
If $$\vec{a}\times(\vec{b}\times\vec{c})+(\vec{a}\cdot\vec{b})\vec{b}=(4-2\lambda-\sin\alpha)\vec{b}+(\lambda^2-1)\vec{c}$$ and $(\vec{c}\cdot\vec{c})\vec{a}=\vec{c}$ where $\vec{b},\vec{c}$ are ...
- 3,381
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Finding the equation of 2D lines
Find the equation of a 2D line which...
A) Passes through the point A(0,-2) and is perpendicular to the vector v=(-2,-5)
B)Passes through the points A(2,-3) and B(3,-4)
C)Passes through the point A ...
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Help with finding range and equation of a position vector (projectile) [duplicate]
I'm given the position vector:
$$ r(t) = ht \hat\imath + t(v − 5mt) \hat\jmath$$
where $m$ = mass, $h$ = horizontal speed and $v$ = vertical speed.
Then the following data is given:
$$\begin{...
