If `veca=1/(sqrt(10))(3hati+hatk),vecb=1/7(2hati+3hatj-6hatk)`, then the value of `(2veca-vecb).{(vecaxxvecb)xx(veca+2vecb)}` is

Options

A. `-3`
B. 5
C. 3
D. `-5`

Answer

D

Explanation

Given , `a = 1/(sqrt(10)) (hati + hatk)` and `b = 1/(7) (2hati + 3hatj - 6hatk)`
`:. (2a-b) .[(a xx b) xx (a+2b)]`
`= (2a - b).{(a xx b) xx a + (a xx b) xx 2b }`
`= (2a - b) .{(a.a) b - (b.a) a+ 2 (a.b) b - 2(b.b)a}`
`= (2a - b) .{1(b)- (0) a + 2(0) b - 2 (1)a}`
[ `:' a .b = 0` and ` a.a = b = 1`]
`= (2a - b) (b - 2a) = - (4|a|^(2) - 4a. b + |b|^(2))`
`= - {4 - 0 + 1} = - 5`