If `a=hati+2hatk+3hatk, b=-hati+2hatj = hatk` and `c=3hati+hatj`, then p such that `a+pb` is at right angle to c will be

Options

A. 7
B. 9
C. 3
D. 5

Answer

D

Explanation

Given, `a+p b ` is at right angle to c.
`therefore (a+pb)*c=0 rArr a*c+p(b*c)=0`
`rArr 5-p=0 `
`[ because a*c = 3+2 = 5 and b*c=-3+2 = -1] `
`therefore p = 5`