With respect to a rectangular cartesian co-ordinate system three vectors are expressed as : `vec(a)=4hat(i) - hat(j),vec(b)=-3 hat(i) + 2hat(j):vec( c)=-hat(k)` . The unit vector `hat(r)`, along the direction of the sum of these vectors is :

Options

A. `hat(r )=1/sqrt(3) (hat(i) + hat(j) - hat(k))`
B. `hat(r )=1/sqrt(2) (hat(i) + hat(j) - hat(k))`
C. `hat(r )=1/sqrt(3) (hat(i) - hat(j) + hat(k))`
D. `hat(r )=1/sqrt(3) (hat(i) + hat(j) + hat(k))`

Answer

A

Explanation

Here `vec(r )=vec(a) + vec(b) + vec(c)=4hati - hatj -3hati+2hatj-hatk`
`vec(r )=hati + hatj - hatk |vec(r )|=sqrt(1+1+1)=sqrt(3)`
Unit vector, `hat(r )=vec(r)/|vec(r)|=(hati + hatj- hatk)/sqrt(3)`