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If hatn=ahati+bhatj is perpendicualr to ...

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

A

1,0

B

`-2,0`

C

3,0

D

`1/sqrt2,-1/sqrt2`

Text Solution

Verified by Experts

The correct Answer is:
D
`1=sqrt(a^2+b^2), " or " a^2+b^2=1 " "...(i)`
And `(a hati+ b hatj) . (hati+hatj)=0" or " a +b = 0 , " ,or " b = - a`
From (i) , `a^2 +(-a)^2 =1`
or `a^2+(-a)^2=1`
or `a=1/sqrt2 and b = 1/sqrt2`
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