A vector A → is rotated by a small angle ∆ θ radians ∆ θ ≪ 1 to get a new…

A vector A→ is rotated by a small angle ∆θ radians ∆θ≪1 to get a new vector B→ . In that case B→-A→ is :
  1. A→1-∆θ22
  2. 0
  3. A→∆θ
  4. B→∆θ-A→

Solution

B→=A→

B→-A→=A→2+A→2+2A→A→cos180°-∆θ

=A→2+A→2-2A→2cos∆θ

=2A→2-2A→2cos∆θ

=2A→21-cos∆θ

∵1-cos∆θ=2sin2∆θ2

=2A→2×2sin2∆θ2

=2A→sin∆θ2

For small ∆θ, sin∆θ2≃∆θ2

B→-A→=2A→∆θ2

=A→ ∆θ

Asked in: JEE Main 2015 (11 Apr Online)

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