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Two particles P and Q located at the points with coordinates $P (t, t^{3} - 16 t - 3), Q (t + 1, t^{3} - 6 t - 6)$ aremoving in a plane. The minimum distance between them in their motion is

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Detailed Solution

${PQ}^{2} = {(t - t - 1)}^{2} + {(t^{3} - 16 t - 3 - t^{3} + 6 t + 6)}^{2} S = {PA}^{2} = 1 + (- 10 t + 3)^{2} {(3 - 10 t)}^{2} \geq 0 1 + {(3 - 10 t)}^{2} \geq 1 {PQ}^{2} \geq 1 PQ \geq 1$

$∴$ min value of PQ is 1

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