Two vectors each have magnitude P. Their resultant's magnitude exceeds P by 0.732P. If the angle between the vectors increases by half its initial value, their difference has magnitude √x·P. Find x.
Physics · Mixed Chapter
JEE Main Practice

Question

Two vectors each have magnitude P. Their resultant's magnitude exceeds P by 0.732P. If the angle between the vectors increases by half its initial value, their difference has magnitude √x·P. Find x.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: Equal vectors give resultant R = 2P cos(θ/2). Given R/P = 1+0.732 ≈ √3, infer cos(θ/2)=√3/2. Step 2: Original angle θ≈60°. Increased by half gives new angle 90°. Step 3: Difference magnitude D = 2P sin(90°/2)=√2P. Step 4: Comparing with √xP gives x = 2.