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in Physics and measurements by (60 points)
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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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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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