Question

Given that A + B = R and A² + B² = R². The angle between A and B is:

• A. 0
• B. π/4
• C. π/2
• D. π

Hint:

Always use the identity (A+B)² = A² + B² + 2ABθ to find the angle between two vectors.

Answer 1

The Correct Option is C

Step 1: Using the vector identity, R² = (A + B)² = A² + B² + 2ABθ
Step 2: Given that A² + B² = R², substitute in the above equation: A² + B² = A² + B² + 2ABθ
Step 3: Simplifying, 2ABθ = 0 Since A ≠ 0 and B ≠ 0, θ = 0
Step 4: Therefore, θ = (π)/(2)