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Let veca= 2 hati + 3hatj - 6hatk, vecb =...

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

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)`

Text Solution

Verified by Experts

The correct Answer is:
b
`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)`
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