The unit vector perpendicular to vectors `a=3hati+hatj` and `=2hati-hatj-5hatk` is

Options

A. `+-((hati-3hatj+hatk))/(sqrt(11))`
B. `+-(3hati+hatj)/(sqrt(11))`
C. `+-((2hati-hatj-5hatk))/(sqrt(30))`
D. none of these

Explanation

(a) `a=3hati+hatj` and `b=2hati-hatj-5hatk`
`axxb=|(hati, hatj, hatk),(3,1,0),(2,-1,-5)|=(-5)hati-(-15-0)hatj+(-3-2)hatk`
`=-5hati+15hatj-5hatk`
`R=axxb=-5(hati-3hatj+hatk)`
`hatR=(hati-3hatj+hatk)/(sqrt((1)^(2)+(-3)^(2)+(1)^(2)))=(hati-3hatj+hatk)/(sqrt(11))`