If `hatn=ahati+bhatj` is perpendicualr to the vector `(hati+hatj)`, then the value of a and b may be:

Options

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

Answer

D

Explanation

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