TS EAMCET · Maths · Three Dimensional Geometry
Two particles \(P\) and \(Q\) located at the points with coordinates \(P\left(t, t^3-16 t-3\right)\), \(Q\left(t+1, t^3-6 t-6\right)\) are moving in a plane. The minimum distance between them in their motion is
- A 1
- B 5
- C 169
- D 49
Answer & Solution
Correct Answer
(A) 1
Step-by-step Solution
Detailed explanation
Here, \[ \begin{aligned} & P Q=\sqrt{(t+1-t)^2+\left(t^3-6 t-6-t^3+16 t+3\right)^2} \\ & =\sqrt{1+(10 t-3)^2} \\ \therefore & P Q^2=1+(10 t-3)^2 \geq 1 \end{aligned} \] Hence, minimum value of \(P Q\) is 1 .
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