Let `vec(p),vec(q),vec(r)` be three unit vectors such that `vec(p)xxvec(q)=vec(r)`. If `vec(a)` is any vector such that `[vec(a),vec(q),vec(r )]=1,[vec(a),vec(r),vec(p )]=2`, and `[vec(a),vec(p),vec(q )]=3`, then `vec(a)=`

Options

A. `vec(p)+3vec(q)+vec(r )`
B. `vec(3p)+vec(2q)+vec(r )`
C. `vec(p)-vec(2q)-vec(3r)`
D. `vec(p)+vec(2q)+vec(3q)`

Answer

D

Explanation

Given that `vec(p)xxvec(q)=vec(r )`
`implies (vec(p)xxvec(q)).vec(r )=|vec(r )|^(2)implies[vec(p)vec(q)vec(r )]=1`
Let `(a)=xvec(p)+yvec(q)+zvec(r)....(1)`
Take dot product in equation (1)both sides
with `vec(p)xxvec(q), vec(q)xxvec(r)` and `vec(r )xxvec(p)` we get
`x=1, y=2, z=3.`