1
vote
0answers
34 views

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 $13x+y-5z = 0$?
0
votes
1answer
33 views

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 ...
2
votes
1answer
33 views

How do you find the max value of a length of a vector?

I have a vector $v = 7j$ and a vector $u$ with a length of 5 that starts at the origin and rotates in the $xy$-plane. How am I supposed to find the max value of the length of the vector $|u \times ...
0
votes
3answers
69 views

Cross product of vector functions

I was trying to make sense of a problem when I stumbled upon this on yahoo answers. I was just wondering if it was correct. If it is, can you please maybe explain why? ${\bf r}'(t) = \langle -5 \cos ...
2
votes
1answer
98 views

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 ...
1
vote
2answers
93 views

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 ...
0
votes
1answer
72 views

Another Cross Product

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 ...
2
votes
2answers
155 views

Vectors question

I'm trying to prove whether the followings statements are true or not. I would appreciate your help, as I'm not sure how to begin. Given: $ u,x_n \in \mathbb{R}^3$ and for every $n$, let $x_{n+1}=u ...
1
vote
1answer
4k views

Fleming's “right-hand rule” and cross-product of two vectors

I have been throwing around hand gestures for the past hour in a feeble attempt at trying to solve this question involving a cross product of two vectors $a$ x $b$. So far, I haven't found any ...