If `ahati +bhatj` is a unit vector and it is perpendicular to `hati +hatj` , then value of a and b is

Options

A. `1, 0`
B. `-2, 0`
C. `3, 0`
D. `(1)/(sqrt2), - (1)/(sqrt2)`

Answer

4

Explanation

`hatn=ahati+bhatj rArr sqrt(a^(2) + b^(2))= 1 or a^(2) + b^(2)= 1`
`(ahati+bhatj)*(hati+hatj)=0 rArr a+ b=0`
`a^(2) + b^(2) =1 rArr a = (1)/(sqrt2), b= (-1)/(sqrt2)`