1.

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

Answer»

`(-3, 2)`
`(2,-3)`
`(-2, 3)`
`(3, -2)`

SOLUTION :SINCE,the givenvectors 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 solvingEqs. (i) and (ii), we get
`mu = 2` and `lambda = - 3`
`:. (lambda, mu) = (-3,2)`


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