If ` vec a=4 hat i+3 hat j+ hat k\ a n d\ vec b= hat i-2 hat k\ t h e n\ fin d\ |2 vec bxx vec a|dot`

Explanation

It is given that

`vec{a}=(4hat{i}+3 hat{j}+ hat{k})`
`2vec{b}=(2hat{i}+0hat{j}-4hat{k})`

`2vec{b} times vec{a}=|hat{i} \ hat{j} \ hat{k}\ 2 \ 0 \ -4 \ 4\ 3\ 1|`
`=hat{i}(0+12)-hat{j}(2+16)+hat{k}(6-0)`

`=-12 hat{i}-18 hat{j}+6hat{k}`

`Rightarrow|2 vec{b} times vec{a}|=sqrt{(12)^{2}+(-18)^{2}+(6)^{2}}`

`=sqrt{504}`