If the vectors `hati-3hatj+2hatk,-hati+2hatj` represents the diagonals of a parallelogram, then its area will be

Options

A. `sqrt(21)`
B. `(sqrt21)/(2)`
C. `2sqrt(21)`
D. `(sqrt21)/(4)`

Answer

B

Explanation

Let `veca=hati-3hatj+2hatk,vecb=-hati+2hatj`
Now, `veca xx vecb=|{:(hati,-hatj,-hatk),(1,-3,0),(-1,2,0):}|`
`=- hati-2hatj-hatk`
Hence , requird area `=(1)/(2)| veca xx vecb|`
`=(1)/(2)sqrt(16+4+1)=(sqrt(21))/(2)`