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

Explanation

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

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

`=0hat{i}-0hat{j}+8hat{k}`

Area of paralellogram`Rightarrow| vec{a} times vec{b}|=sqrt{(0)^{2}+(-0)^{2}+(6)^{2}}`

`=sqrt{6^2}=6`