If the vectors `veca=hati-hatj+2hatk, vecb=2hati+4hatj+hatk and vecc=lamda hati+hatj+muhatk` are mutually orthogonal `then (lamda, mu)=` (A) (-2,3) (B) (3,-2) (C) (-3,2) (D) (2,-3)

Options

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

Answer

A

Explanation

Condition for orthogonal a.c =0
` ( hati - hatj +2hatk ).(lamda hati +hatj +mu hatk )=0`
`implies lamda -1+2 mu =0`
`implies lamda +2 mu =1`
`b.c=0`
` implies 2 lamda +4+mu =0`
`implies 2 lamda +mu =-4`
on solving Eqs,(i) and (ii) we get
`lamda =- 3 , mu = 2 `