If the vectors `a=hati-hatj+2hatk, b=2hati+4hatj+hatk` and `c=lambdahati+hatj+mu hatk` are mutually orthogonal, then `(lambda, mu)` is equal to

Options

A. `(-3, 2)`
B. `(2,-3)`
C. `(-2, 3)`
D. `(3, -2)`

Answer

A

Explanation

Since, the given vectors are mutually orthogonal, therefore
`a.b = 2 - 4 + 2 = 0`
`a .c = lambda - 1 + 2 mu = 0 "…."(i)`
and `b .c = 2lambda + 4 + mu = 0 "….."(ii)`
On solving Eqs. (i) and (ii) , we get
`mu = 2` and `lambda = - 3`
`:. (lambda, mu) = (-3,2)`