Diagonals of a parallelogram are respresented by vectors `vecA = 5hati - 4hatj + 3hatk and vecB = 3hati +2hatj - hatk`. Area of the parallelogram is :

Options

A. `sqrt171` unit
B. `sqrt72` unit
C. 171 unit
D. 72 unit

Answer

D

Explanation

Area of parallelogram `=1/2 |vecA xx vecB|`
`|vecA xxvecB|=|{:(hati, hatj, hatk),(5, -4, 3),(3,2,-1):}|`
`hati(4-6) -hatj (-5-9) +hatk(10+12)`
`-2hati+14 hatj +22katk`
`vecAxxvecB=sqrt(4+196+484)`
`=2 sqrt171`
Area `=1/2xx2 sqrt171=sqrt 171`