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Given three vectors a=6hati-3hatj,b=2hat...

Given three vectors `a=6hati-3hatj,b=2hati-6hatj and c=-2hati+21hatj` such that `alpha=a+b+c`. Then, the resolution of the vector `alpha` into components with respect to a and b is given by

A

3a-2b

B

3b-2a

C

2a-3b

D

a-2b

Text Solution

Verified by Experts

The correct Answer is:
C
`alpha=a+b+c=6hati+12hatj`
Let `alpha=xa+ybimplies 6x+2y=6`
and `-3x-6y=12`
`therefore x=2,,y=-3`
`therefore alpha=2a-3b`.
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