The unit vector parallel to the resultant of the vectors `vec(A) = hat(i) + 2 hat(j) - hat(k)` and `vec(B) = 2 hat(i) + 4 hat(j) - hat(k)` is

Options

A. `(1)/(49) (7 hat(i) + 6 hat(j) - 2 hat(k))`
B. `(1)/(7) (3 hat(i) + 6 hat(j) - 2 hat(k))`
C. `(1)/(49) (3 hat(i) + 6 hat(j) - 2 hat(k))`
D. `(1)/(7) (7 hat(i) + 6 hat(j) - 2 hat(k))`

Answer

B

Explanation

`vec(A) + vec(B) = 3i + 6 j - 2k`
`|vec(A) + vec(B)| = sqrt((3)^(2) + (6)^(2) + (-2)^(2)) = 7`
Unit vector along `(vec(A) + vec(B)) = (vec(A) + vec(B))/(|vec(A) + vec(B)|) = (1)/(7) ( 3i + 6j - 2k)`