The position vectors of vertices of a `DeltaABC` are `4hati - 2 hatj , hati + 4hatj - 3hatk` and `-hati + 5hatj + hatk` respectively , then `angleABC` is equal to

Options

A. `(pi)/(6)`
B. `(pi)/(4)`
C. `(pi)/(3)`
D. `(pi)/(2)`

Answer

D

Explanation

Here , `vec(AB) = - 3hati + 6hatj - 3hatk , vec(BC) = - 2hati + hatj + 4 hatk `
and `vec(AB ) * vec(BC) = 6 + 6 - 12 = 0`
`implies angle ABC = (pi)/(2)`