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    Question

    If x = r sin A cos B, y = r sin A sin B and z = r cos A,

    then find xĀ² + yĀ² + zĀ².
    A 2rĀ² Correct Answer Incorrect Answer
    B 3/2 rĀ² Correct Answer Incorrect Answer
    C rĀ² Correct Answer Incorrect Answer
    D rĀ²(cosĀ² B + cosĀ² A) Correct Answer Incorrect Answer

    Solution

    x = r sin A cos B, y = r sin A sin B z = r cos A Now, xĀ² + yĀ² + zĀ² = (r sin A cos B) Ā² + (r sin A sin B) Ā² + (r cos A)2 = r2 sin2 A (cosĀ² B + sinĀ² B) + r2 cosĀ² A = rĀ² sinĀ² A + r2 cosĀ² A = rĀ² (sinĀ² A + cosĀ² A) = r2

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