By parallelogram law of vector addition, angle made by resultant with P is given by; tan‌α=
Q‌sin‌θ
P+Q‌cos‌θ
Here α=90°. So ; tan‌90°=∞=
Q‌sin‌θ
P+Q‌cos‌θ
⇒P+Q‌cos‌θ=0 or Q‌cos‌θ=−P Now, magnitude of resultant, R=√P2+Q2+2PQ‌cos‌θ Here, we have R=2P and Q‌cos‌θ=−P and Q=10m So, 2P=√P2+100−2P2 ⇒4P2=100−P2⇒5P2=100 or P=√20=2√5m Magnitude of P is 2√5m.