Question

If vector A+vectorB are such that |vectorA+vectorB|=|vectorA|=|vectorB|,then |vectorA-vectorB| may be equated to

Answer 1

Answer:

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Answer 2

Given: |A⃗ +B⃗ | = |A⃗ | = |B⃗ |

Now; |A+B|² = (A²+B²+2ABcosθ)

A² = A²+A² +2A²cosθ

cosθ = –A²/2A²= –1/2

θ = cos⁻¹(–1/2) = 120°

As; |A⃗ – B⃗ | = √(A²+B²+2ABcos(180°-θ)

or |A⃗ – B⃗ | = √(A²+B²–2ABcosθ)

|A⃗ – B⃗ | = √(2A²–2A²cosθ)

|A⃗ – B²| = A√2 √(1–cosθ)

|A⃗ – B⃗ | = A√2 √(1–2cos²(θ/2)+1)

|A⃗ – B⃗ | = A√(2×2) sin(θ/2)

|A⃗ – B⃗ | = 2A sin60°

|A⃗ – B⃗ | = 2√3A/2

∴ |A⃗ – B⃗ | = √3(|A⃗ |)