Question

Find v x w if v=-9i+2j-3k and w=8i-3j+8k

Answer 1

A

Explanation:

Edge

Answer 2

The cross product satisfies

`\mathbf i*\mathbf i=\mathbf j*\mathbf j=\mathbf k*\mathbf k=\mathbf 0`

`\mathbf i*\mathbf j=\mathbf k`

`\mathbf j*\mathbf k=\mathbf i`

`\mathbf k*\mathbf i=\mathbf j`

The cross product is anti-commutative, so that for any two vectors
`\mathbf a` and
`\mathbf b`,
`\mathbf a*\mathbf b=-(\mathbf b*\mathbf a)`, and

`\mathbf j*\mathbf i=-\mathbf k`

`\mathbf k*\mathbf j=-\mathbf i`

`\mathbf i*\mathbf k=-\mathbf j`

It's also distributive, which means we have

`(-9\,\mathbf i+2\,\mathbf j-3\,\mathbf k)*(8\,\mathbf i-3\,\mathbf j+8\,\mathbf k)`

`=-72(\mathbf i*\mathbf i)+16(\mathbf j*\mathbf i)-24(\mathbf k*\mathbf i)`

`\,+27(\mathbf i*\mathbf j)-6(\mathbf j*\mathbf j)+9(\mathbf k*\mathbf j)`

`\,-72(\mathbf i*\mathbf k)+16(\mathbf j*\mathbf k)-24(\mathbf k*\mathbf k)`

`=(16-9)(\mathbf j*\mathbf k)+(72-24)(\mathbf k*\mathbf i)+(27-16)(\mathbf i*\mathbf j)`

`=7\,\mathbf i+48\,\mathbf j+11\,\mathbf k`