With respect to a rectangular Cartesian co-ordinate system, three vectors are expressed as `vec a = 4hati -hatj, vec b =-3hati +2hatj, vec c=-hatk` where `hati, hatj, hatk` are unit vectors, along the x, y and z-axes respectively. The unit vector `hatr` along the direction of the sum of these three vectors is given by

Options

A. `hatr=1/sqrt3(hati+hatj-hatk)`
B. `hatr=1/sqrt2(hati+hatj-hatk)`
C. `hatr=1/sqrt3(hati-hatj+hatk)`
D. `hatr=1/sqrt3(hati+hatj+hatk)`

Answer

A

Explanation

The sum of three vectors , `vecr = veca + vecb + vecc`
`=(4hati -hatj) +(-3hati+2hatj)+(-hatk)=hati+hatj+hatk`
Unit vector, `hatr=vecr/r=(hati+hatj-hatk)/(sqrt(1^2+1^2+(-1)^2))=1/sqrt3(hati+hatj-hatk)`