JEE Mains · Maths · STD 12 - 11. three dimension geometry
One vertex of a rectangular parallelopiped is at the origin \(O\) and the lengths of its edges along \(x , y\) and \(Z\) axes are \(3,4\) and \(5\) units respectively. Let \(P\) be the vertex \((3,4,5)\). Then the shortest distance between the diagonal \(OP\) and an edge parallel to \(Z\) axis, not passing through \(O\) or \(P\) is:
- A \(\frac{12}{\sqrt{5}}\)
- B \(\frac{12}{5 \sqrt{5}}\)
- C \(12 \sqrt{5}\)
- D \(\frac{12}{5}\)
Answer & Solution
Correct Answer
(D) \(\frac{12}{5}\)
Step-by-step Solution
Detailed explanation
Equation of OP is \(\frac{x}{3}=\frac{y}{4}=\frac{z}{5}\) \(\begin{array}{ll}a_1=(0,0,0) & a_2=(3,0,5) \\b_1=(3,4,5) & b_2=(0,0,1)\end{array}\) Equation of edge parallel to \(z\) axis…
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