The three vectors `hat i+hat j,hat j+hat k, hat k+hat i` taken two at a time form three planes, The three unit vectors drawn perpendicular to these planes form a parallelopiped of volume: ________________

Options

A. `1//3`
B. 4
C. `(3sqrt3)//4`
D. `4sqrt3`

Answer

d

Explanation

` (hati + hatj) xx (hatj xx hatk ) =hati -hatj + hatk ` so that unit vector perpendicular to the plane of `hati +hatj and hatj + hatk ` is `1/sqrt3 (hati -hatj +hatk)`
Required volume = ` 3/ sqrt3 |{:(1,-1,1),(1,1,-1),(-1,1,1):}|= 4sqrt3`