I have these two questions regarding the Cross Product.
1.) You are looking down at a map. A vector $u$ with $|u| = 3$ points north and a vector $v$ with $|v| = 10$ points northeast.
What is $|u \times v|$ = ?
2.) If $v \times w = \langle −1,0,5 \rangle$ and $v \cdot w = 4$, find $\tan(x)$, where $x$ is the angle between $v$ and $w$. Find the angle.
I'm confused as to how I should set up $| u \times v | = |u| |v| \sinθ$ in order to solve these two questions. Any ideas?
Best Answer
Hint:angle between v and V is $45^0$ and $$|u| = 3|v| = 10 $$ then put in and find $u\times v$
$$\lvert u\times v\rvert = \lvert u\rvert\lvert b\rvert \lvert\sin(\theta)\rvert $$ for second part use: $$\frac{|u\times v|}{|u.v|}=tan(\theta) $$