Two vectors `vec(P) " and "vec(Q)` are added, the magnitude of resultant is 15 units. If `vec(Q)` is reversed and added to `vec(P)` resultant has a magnitude `sqrt(113)` units. The resultant of `vec(P)` and a vector perpendicular ` vec(P)` and equal in magnitude to` vec(Q)` has a magnitude

Options

A. 13 units
B. 17 units
C. 19 units
D. 20 units

Answer

A

Explanation

`P^(2)+Q^(2)+2PQ cos theta =225`…(i)
`P^(2)+Q^(2)-2PQcos theta =113 ` …..(ii)
By adding (i) & (ii) `2(P^(2)+Q^(2))=338`
`P^(2)+Q^(2)=169implies sqrt(P^(2)+Q^(2))=13`