Given three vectors veca=6hati-3hatj,vec...

Given three vectors `veca=6hati-3hatj,vecb=2hati-6hatj and vecc=-2hati+21hatj` such that `vecalpha=veca+vecb+vecc`. Then the resolution of te vector `vecalpha` into components with respect to `veca and vecb` is given by (A) `3veca-2vecb` (B) `2veca-3vecb` (C) `3vecb-2veca` (D) none of these

A

`3veca- 2vecb`

B

`3vecb - 2veca `

C

`2 veca - 3vecb`

D

`veca - 2vecb `

Text Solution

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The correct Answer is:

C

`vecalpha = veca + vecb + vecc = 6hati+ 12hatj`
Let `vecalpha = xveca + yvecb rArr 6x + 2y =6`
and `-3x - 6y = 12 `
`therefore x = 2, y =-3`
`therefore " " vecalpha = 2 veca - 3 vecb`

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