MP Board · Class 11 · Physics · Motion in a PlaneIf the magnitude of the sum of two vectors is equal to the magnitude of their difference, what is the angle between them?
Step-by-Step Solution
Given $|\vec{A} + \vec{B}| = |\vec{A} - \vec{B}|$, squaring both sides gives $A^2 + B^2 + 2AB\cos\theta = A^2 + B^2 - 2AB\cos\theta$, which simplifies to $4AB\cos\theta = 0$, meaning $\cos\theta = 0$ or $\theta = 90^\circ$.
Detailed Options Breakdown
Option : $0^\circ$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Motion in a Plane.
Option 1: $60^\circ$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Motion in a Plane.
Option 2: $90^\circ$ (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 3: $180^\circ$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Motion in a Plane.
💡 Study Guide: This question tests core syllabus concepts from Motion in a Plane. For formulas, key summaries, and mock exam reference guides, read the full Motion in a Plane Revision Notes.