Find the area of the parallelogram whose diagonals are: `4 hat i- hat j-3 hat k\ a n d-2 hat i+ hat j-2 hat k`

Explanation

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

`vec{a} times vec{b}=|hat{i} \ hat{j} \ hat{k}\ 4\ -1 \-3\ -2\1\ -2|`
`=hat{i}(2+3)-hat{j}(-8-6)+hat{k}(4-2)`

`=-5hat{i}+14hat{j}+2hat{k}`

`Rightarrow| vec{a} times vec{b}|=sqrt{(5)^{2}+(14)^{2}+(2)^{2}}`

`=sqrt{225}=15`

Area of parallelogram`=1/2| vec{a} times vec{b}|`

`=1/2 times 15 sq. units`