Two vectors X → and Y → have equal magnitude. The magnitude of ( X → - Y → ) is n…

Two vectors X→ and Y→ have equal magnitude. The magnitude of (X→-Y→) is n times the magnitude of (X→+Y→). The angle between X→ and Y→ is :
  1. cos-1-n2-1n2-1
  2. cos-1n2-1-n2-1
  3. cos-1n2+1-n2-1
  4. cos-1n2+1n2-1

Solution

Given X=Y

X2+Y2-2×Ycosθ

=nX2+Y2+2×Ycosθ

Square both sides

2X2(1-cosθ)=n2·2X2(1+cosθ)

1-cosθ=n2+n2cosθ

cosθ=1-n21+n2

θ=cos-1n2-1-n2-1

Asked in: JEE Main 2021 (25 Jul Shift 2)

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