Suppose the position vector r(t) of an object moving in 3-space and the corresponding velocity and acceleration vectors v(t) and a(t) satisfy
(i) a(t) is parallel to r(t) for all t, and
(ii) r(0) × v(0) = c (a nonzero constant vector).
Find r(t) × v(t) and c . r(t) for all t.

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The Answer of Suppose the position vector r(t) of an object moving in 3-space and the corresponding velocity and acceleration vectors v(t) and a(t) satisfy
(i) a(t) is parallel to r(t) for all t, and
(ii) r(0) × v(0) = c (a nonzero constant vector).
Find r(t) × v(t) and c . r(t) for all t.

Suppose the Position Vector R(t) of an Object Moving in 3-Space