Question

If the diagonals of a parallelogram are represented by the vectors ` 3hati + hatj -2hatk and hati + 3hatj -4hatk`, then its area in square units , is
A. ` 5sqrt3`
B. `6sqrt3`
C. `sqrt42`
D. `sqrt42`

Answer 1

Correct Answer - C
Let `veca = 3hati + hatj -2hatk and vecb = hati + 3hatj -4hatk` . Then
` veca xx vecb = |{:( hati, hatj , hatk),(3,1,-2),(1,3,-4):}| = 2hati+10 hatj + 8hatk`
` Rightarrow |veca xx vecb| = sqrt( 4 + 100 + 64) = sqrt168 = 2sqrt42`
Required area =` 1/2 |veca xx vecb| = sqrt42` sq unit.