If `vec(A) = 3 hat(i) + 6 hat(j) - 2hat(k)` , the directions of cosines of the vector `vec(A)` are

Options

A. `(3)/(7) ,(6)/(7) ,(2)/(7)`
B. `(3)/(7) ,(6)/(7) , (-2)/(7)`
C. `(6)/(7) ,(2)/(7) ,(3)/(7)`
D. `(2)/(7) ,(3)/(7) ,(6)/(7)`

Answer

B

Explanation

If `vec (r ) = x hat(i) + y hat(j) + z hat(k) , r = sqrt(x^(2) + y^(2) + z^(2))`
`alpha , beta , gamma` : angles made by `vec(r )` with coordinates axes
`cos alpha = (x)/( r) , cos beta = (y) /( r ) , cos gamma = (z)/( r )`
Direction cosines ,` cos alpha , cos beta , cos gamma`
`vec(A) = 3 i + 6 j - 2k , |vec(A)|= A = sqrt((3)^(2) + (6)^(2) + (-2)^(2)) = 7`
`cos alpha = (3)/(7) , cos beta = (6)/(7) , cos gamma = (-2)/(7)`