The area of the parallelogram whose adjacent sides are `hati-3hatj+hatk and hati+hatj+hatk` is

Options

A. `4sqrt2`
B. `-4sqrt2`
C. `4sqrt3`
D. None of these

Answer

B

Explanation

Let , `a=hat(i)-3hat(j)+hat(k) and b=hat(i)+hat(j)+hat(k)`
`therefore` Area of parallelogram having adjacent sides, a and b is
`|a xxb|=|{:(hat(i),hat(j),hat(k)),(1,-3,1),(1,1,1):}|`
`=|hat(i)(-3-1)-hat(j)(1-1)+hat(k)(1+3)|`
`=|-4hat(i)+4hat(k)=sqrt((-4)^2+4^2)=sqrt(16+16)`
`=sqrt(32)=4sqrt(2)` sq units.