The unit vector perpendicular to `hati-hatj` and coplanar with `hati+2hatj` and `hati+3hatj` is

Options

A. `(2hati-5hatj)/(sqrt(29))`
B. `2hati+5hatj`
C. `1/(sqrt(2))(hati+hatj)`
D. `hati+hatj`

Answer

C

Explanation

Let vector `a=xhati+yhatj`
`a` is coplanar with `hati+2hatj` and `hati+3hatj`
`:.a=(hati+K2hatj)+lamda(hati+3hatj)`
`impliesa=(1+lamda)hati+(2+3lamda)hatj`
Since `a` is perpendicular to `hati-hatj`
`[(1+lamda)hati+(2+3lamda)hatj][hati-hatj]=0`
`implies1+lamda-2-3lamda=0implieslamda=(-1)/2`
`:.a=(1-1/2)hati+(2-3/2)hatj`
`=1/2hati+1/2hatj=hata=a/(|a|)=(hati+hatj)/(sqrt(2))`