AP EAPCET 08-Jul-2022 Shift 2 Paper

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.