Find the area of the parallelogram determined by the vectors: `2 hat i+ hat j+3 hat k\ a n d\ hat i- hat j`

Explanation

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

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

`=3hat{i}+3hat{j}-3hat{k}`

Area of paralellogram`Rightarrow| vec{a} times vec{b}|=sqrt{(3)^{2}+(3)^{2}+(-3)^{2}}`

`=sqrt{27}=3 sqrt{3}`