The resultant of two vectors A and B is perpendicular to A and its magnitude is half that of B. The angle between vectors A and B i s ______°.
Physics · Mathematical tools and vector
JEE Mains 2024 09 Apr Evening Shift

Question

The resultant of two vectors A and B is perpendicular to A and its magnitude is half that of B. The angle between vectors A and B i s ______°.

G1 Physics · Accepted Answer

Let the resultant be: R = A + B Given: R is perpendicular to A. Therefore: A · R = 0 A · (A + B) = 0 A² + AB cosθ = 0 ...(1) Also: |R| = B/2 Using: R² = A² + B² + 2AB cosθ and equation (1), the geometry gives: B cos60° = B/2 So the angle between B and the resultant is 60°. Since resultant is perpendicular to A, the angle between A and B is: 90° + 60° = 150°