The algebraic sum of two co-initial vectors is 16 units . Their vector sum is 8 units and the resultant of the vectors are perpendicular to the smaller vector. Then magnitudes of the two vectors are -

Step-by-step solution

P + Q = 16 (i) P 2 + Q 2 + 2 P Q cos θ = 64 (ii) tan 90 ο = Q sin θ P + Q cos θ ⇒ P + Q cos θ = 0 cos θ = - P Q From Eq. (ii) P 2 + Q 2 + 2 PQ cos θ = 64 P 2 + Q 2 + 2.P.Q - P Q = 64 - P 2 + Q 2 = 64 Q + P Q - P = 64 as P + Q = 16 Q - P = 4 Solving we get 2 Q = 20 Q = 10 units P = 6 units