Let `veca= 2 hati + 3hatj - 6hatk, vecb = 2hati - 3hatj + 6hatk and vecc = -2 hati + 3hatj + 6hatk`. Let `veca_(1)` be the projection of `veca on vecb and veca_(2)` be the projection of `veca_(1) on vecc` . Then
`veca_(2)` is equal to

Options

A. `943/49 (2 hati - 3hatj - 6hatk)`
B. `943/(49^(2)) (2 hati - 3hatj - 6hatk)`
C. `943/49 (-2 hati + 3hatj + 6hatk)`
D. `943/(49^(2)) (-2 hati + 3hatj + 6hatk)`

Answer

b

Explanation

`veca_(1)[(2hati+3hatj-6hatk)((2hati-3hatj + 6hatk))/7](2hati-3hatj + 6hatk)/7`
`(-41)/49(hati-3hatj + 6hatk)`
`veca_(2) (-41)/49((2hati-3hatj + 6hatk).((-2hati+3hatj+6hatk))/7)`
`xx ((-2hati + 3hatj = 6hatk))/7`
`(-41)/((49)^(2))(-4-9+36) (-2hati+3hatj + 6hatk)`
`943/(49^(2))(2hati -3hatj - 6hatk)`