The magnitudes of vectors A, B and C are 3, 4 and 5 units respectively. If $\vec{A}+\vec{B}=\vec{C}$ , the angle between $\vec{A}$ and $\vec{B}$ is:
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Question

The magnitudes of vectors A, B and C are 3, 4 and 5 units respectively. If A ⃗ + B ⃗ = C ⃗ \vec{A}+\vec{B}=\vec{C} A + B = C , the angle between A ⃗ \vec{A} A and B ⃗ \vec{B} B is:

G1 Physics · Accepted Answer

Step 1: Since C=A+B, C²=A²+B²+2AB cosθ. Step 2: Substitute 5²=3²+4²+2×3×4 cosθ. Step 3: 25=25+24 cosθ, so cosθ=0 and θ=π/2. Final answer: A.