Mathematics in Physics

JEE Main level, single correct, medium

27 of 121

Question 27 of 121

Two vectors P⃗\vec{P} and Q⃗\vec{Q} have equal magnitudes. If the magnitude of P⃗+Q⃗\vec{P}+\vec{Q} is nn times the magnitude of P⃗−Q⃗,\vec{P}-\vec{Q}, then angle between P⃗\vec{P} and Q⃗\vec{Q} is

Show answer and solution

Answer: (D) cos⁡−1(n2−1n2+1){\cos }^{-1}\left(\dfrac{{n}^{2}-1}{{n}^{2}+1}\right)

∣P⃗∣=∣Q⃗∣=x…(i)|\vec{P}|=|\vec{Q}|=x\ldots \left(i\right)
∣P⃗+Q⃗∣=n∣P⃗−Q⃗∣|\vec{P}+\vec{Q}|=n|\vec{P}-\vec{Q}|
P2+Q2+2PQcos⁡θ=n2(P2+Q2−2PQcos⁡θ){P}^{2}+{Q}^{2}+2PQ\cos \theta ={n}^{2}\left({P}^{2}+{Q}^{2}-2PQ\cos \theta \right)
Using(i)(i) in above equation,
cos⁡θ=n2−11+n2\cos \theta =\dfrac{{n}^{2}-1}{1+{n}^{2}}
θ=cos⁡−1(n2−1n2+1)\theta ={\cos }^{-1}\left(\dfrac{{n}^{2}-1}{{n}^{2}+1}\right)

JEE Main question paper PDF

Open a shift to read the full paper on this page, or download it.

JEE Main 2025 Apr 2 Shift 1 question paper

Open Download PDF

Opening paper…

Explain it as a whiteboard videoStep-by-step, in Hinglish or English. Your first video needs no login.Solved it on paper but got it wrong?Upload a photo of your working. Mistake Doctor marks the exact line that broke.

More Physics practice

JEE Main Physics practice question on Mathematics in Physics (Addition and Subtraction of Vectors), with the answer and a step-by-step solution. Scan a question from your own book or paper to get a whiteboard video.