Let `veca = 2hati+lambda_1 hatj+3hatk`, `vec(b)=4hati+(3-lambda_2) hatj+6hatk` and `vec(c)=3hati+6hatj+(lambda_3-1)hatk` be three vectors such that `vec(b)=2 vec(a)` and `vec(a)` is perpendicular to `vec(c)` then a possible value of `((lambda)_1,(lambda)_2,(lambda)_3)` is:

(a) `(1,3,1)`
(b) `((-1/2),4,0)`
(c) `(1,5,1)`
(d) `((1/2), 4, -2)`

Options

A. (1,3,1)
B. (1,5,1)
C. `(-1/2,4,0)`
D. `(1/2,4,-2)`

Answer

C