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The magnitude of the vectors \( \vec{A}, \vec{B} \) and \( \vec{C} \) are 3,4 and 5 units respectively. If \( \vec{A}+\vec{B}=\vec{C} \), then the angle between \( \vec{A} \) and \( \vec{B} \) is |
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Answer» Given \(\vec A = 3\) \(\vec B = 4\) \(\vec C = 5\) \(\vec A + \vec B = \vec C\) Squaring both sides \(|\vec A|^2 + |\vec B|^2 + 2\vec A.\vec B = \vec C .\vec C\) \(|\vec A|^2 + |\vec B|^2 + 2|\vec A||\vec B| \,cos \theta = |\vec C|^2\) \((3)^2 + (4)^2 + 2\times 3 \times 4 \, cos \theta = (5)^2\) \(cos\theta = 0\) \(\theta = 90° \) |
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