If `veca=2hati + hatj+ hatk, vecb= hati+ 2hatj + 2hatk,vecc = hati+ hatj + 2hatk and (1 + alpha) hati+ beta(1+ alpha)hatj+gamma(1+alpha)(1 + beta) hatk= vecaxx(vecb xx vecc) , " then " alpha, beta and gamma " are "`

Options

A. `-2,-4,-2/3`
B. `2,-4,2/3`
C. `-2,4,2/3`
D. `2,4,-2/3`

Answer

a

Explanation

` veca xx (vecb xx vecc) = (veca .vecc) vecb -(veca.vecb) vecc`
` = 5 (hati + 2hatj + 2hatk) - 6 (hati + hatj + 2hatk) `
`Rightarrow ( 1 + alpha) hati + beta (1 + alpha) hatj + gamma ( 1+ alpha) (1+beta) hatk`
` = - hati + 4hatj - 2hatk`
` Rightarrow 1 + alpha = -1 , beta = -4 and gamma (n -1) (-3) = (-2)`
` Rightarrow gamma = -2/3`