# Tagged Questions

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### Calculus - Components of a unit vector

Determine the components of a unit vector perpendicular to (0, 3, -5) and (2, 3, 1). I think I should be using either cross or dot product, but am unsure on what to do from there.
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### Cross Product in 3D

Hi! I am currently working on some calc2 online homework problems concerning the cross product. I understand how the cross product works, but I am not sure how to apply it to this question. I know ...
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### How do I solve $F = \nabla\times G$ for $G$?

Given the vector valued function $F(x,y,z) = (xz,-yz,y)$ find $G$ such that $F = \nabla\times G$ I let $G(x,y,z) = (G_1,G_2,G_3)$ and expanded $\nabla \times G$ then equated the components to $F$ but ...
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### Given two lines, how do I find the plane?

$$r_1(t) = \langle t, 2t, 3t\rangle$$ $$r_2(t) = \langle3t, t, 8t\rangle$$ I found $\mathbf{n} = \langle13,1,-5\rangle$ Can I just plug in say $P_0 = (0,0,0)$ and get $13x+y-5z = 0$?
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### Find the length and direction of $u \times v$ and $v \times u$

So I was given two vectors: $u=-8i- 2j- 4k$, and $v=2i+2j+k$. I was able to figure out the cross product of $u\times v$ which is $6i-12k$, and $v \times u$ which is $-6i+12k$. However, I need help ...
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### Showing that a set of points equidistant to two other points form a plane.

Question: if p and q are two distinct points in space, show that the set of points equidistant from p and q form a plane. Work Done: Note: I'm pretty sure this can be done with vectors and cross ...
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### Given $u=(-2,5,3)$ find a unit vector $v$ s.t $|u\times v|$ is maximal, and then a unit vector $w$ s.t $|(u\times v)\cdot w|$ is minimal

This is a similar question to the one I have posted before. The problem is as in the title: Given $u=(-2,5,3)$ find a unit vector $v$ s.t $|u\times v|$ is maximal, and then a unit vector $w$ s.t ...
So I understand most of the properties of cross products. However I ran into a small complication. I get that $i\times j = k$, $j\times k = i$. I also understand that $k \times j = -i$ and that ...