(Solution) - The motion of a particle is defined by the position -(2025 Original AI-Free Solution)

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The motion of a particle is defined by the position vector r = A (cos t + t sin t)i + A(sin t ? t cos t) j, where t is expressed in seconds. Determine the values of t for which the position vector and the
acceleration vector are
(a) Perpendicular,
(b)Parallel.