The area of the parallelogram whose diagonals are the vectors `hati+3hatj- 2hatk and 3hati+hatj-4hatk`

Options

A. `3sqrt(42)` sq units
B. `sqrt(42)` sq untis
C. `2sqrt(42)` sq units
D. None of these

Answer

A

Explanation

Let `a=hat(i)+3hat(j)-2hat(k) and b=3hat(i)+hat(j)-4hat(k)`
The `a xxb=|{:(hat(i),hat(j),hat(k)),(1,3,-2),(3,1,-4):}|`
`=hat(i)(-12+2)-hat(j)(-4+6)+hat(k)(1-9)`
`=-10hat(i)-2hat(j)-8hat(k)`
`therefore` Area of parallelogram `=(1)/(2)|axxb|`
`=(1)/(2)sqrt((-10)^2+(-2)^2+(-8)^2)`
`=(1)/(2)sqrt(100+4+64)=(1)/(2)sqrt(168)`
`=sqrt(42)` sq.units.