Given three vectors ` vec a=6 hat i-3 hat j , vec b=2 hat i-6 hat ja n d vec c=-2 hat i+21 hat j` such that ` vecalpha= vec a+ vec b+ vec cdot` Then the resolution of the vector ` vecalpha` into components with respect to ` vec aa n d vec b` is given by a. `3 vec a-2 vec b` b. `3 vec b-2 vec a` c. `2 vec a-3 vec b` d. ` vec a-2 vec b`

Options

A. 3a-2b
B. 3b-2a
C. 2a-3b
D. a-2b

Answer

C

Explanation

`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`.