Two vectors `vec P and vec Q` are given by
`vec P =3 hati + 4hatj+5hat k`
`vec Q =2hati +2 hatj+3hatk`
What are the direction cosines of the vector `(vec P - vec Q)` ?

Options

A. `(1)/(3), (2)/(3), (2)/(3)`
B. `(2)/(3), (1)/(3), (2)/(3)`
C. `(2)/(5), (3)/(5), (4)/(5)`
D. `(2)/(3), (4)/(3), (5)/(3)`

Answer

A

Explanation

`vec P - vec Q =3hati + 4hatj + 5hatk -2 hati -2hatj-3hatk`
`=hati + 2hatj + 2hatk`
`therefore |vec P - vec Q| = sqrt (1^(2) + 2^(2) + 2^(2)) = sqrt (9) =3`
`therefore` The direction cosines of the vector are `(1)/(3), (2)/(3), (2)/(3)`. [The direction cosines of a vector `vec A` are given by `(Ax)/(A) , (Ay)/(A) and (Az)/(A)`]