Position vector `hatk` is rotated about the origin by angle `135^(@)` in such a way that the plane made bt it bisects the angle between `hati and hatj` . Then its new position is

Options

A. `+-hati/sqrt2+-hatj/sqrt2`
B. `+-hati/2+-hatj/2-hatk/sqrt2`
C. `hati/sqrt2-hatk/sqrt2`
D. none of these

Answer

d

Explanation

Let `vecr` be the new position . Then `vecr= lambdahatk + mu ( hati + hatj) `
` Also, vecr.hatk = - 1/sqrt2 Rightarrow lambda= - 1/sqrt2`
` Also lambda^(2)+ 2mu^(2) = 1 Rightarrow 2mu^92) = 1/2 or mu = +- 1/2`
` vecr = +- 1/2 (hati + hatj) =- hatk/sqrt2`