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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)=`A. `vec(p)+3q+vec(r )`B. `vec(3p)+vec(2q)+vec(r )`C. vec(p)-vec(2q)-vec(3r)`D. `vec(p)+vec(2q)+vec(3q)` |
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Answer» Correct Answer - D 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.` |
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