# Given a cross product: vec(u) xx vec(v) =(:−1,1,−3:) I'm trying to find: (vec(u) −3 vec(v)) xx (vec(u)+2 vec(v)) as a vector.

Given a cross product:
$\stackrel{\to }{u}×\stackrel{\to }{v}=⟨-1,1,-3⟩$
I'm trying to find:
$\left(\stackrel{\to }{u}-3\stackrel{\to }{v}\right)×\left(\stackrel{\to }{u}+2\stackrel{\to }{v}\right)$ as a vector.
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Firetto8w
Let me start if off for you:
$\begin{array}{rl}\left(\stackrel{\to }{u}-3\stackrel{\to }{v}\right)×\left(\stackrel{\to }{u}+2\stackrel{\to }{v}\right)& =\left(\stackrel{\to }{u}-3\stackrel{\to }{v}\right)×u+\left(\stackrel{\to }{u}-3\stackrel{\to }{v}\right)×\left(2\stackrel{\to }{v}\right)\\ & =\left(\stackrel{\to }{u}-3\stackrel{\to }{v}\right)×\stackrel{\to }{u}+2\cdot \left(\left(\stackrel{\to }{u}-3\stackrel{\to }{v}\right)×\stackrel{\to }{v}\right)\end{array}$
In the first line, I used the second rule you wrote, and in the second, I used the first rule you wrote.
Now, continue doing that, and use two extra rules:
$\left(\stackrel{\to }{a}+\stackrel{\to }{b}\right)×\stackrel{\to }{c}=$ something
$\stackrel{\to }{a}×\stackrel{\to }{a}=$ something.