Find the angle between the vectors A and vector B if |A+B|=|A-B|

Question

School work

Answer 1

A = |A|

B = |B|

 

|A + B| = √(A² + B² + 2ABcosθ)

 

|A - B| = √(A² + B² - 2ABcosθ)

 

|A + B| = |A - B| ⇒

 

√(A² + B² + 2ABcosθ) = √(A² + B² - 2ABcosθ)

 

Square both sides.

 

A² + B² + 2ABcosθ = A² + B² - 2ABcosθ

 

2ABcosθ = -2ABcosθ

 

If A ≠ 0 and B ≠ 0, then

 

cosθ = -cosθ ⇒

 

cosθ = 0 ⇒ θ = 90°