Question

Let l₁ be the line in xy-plane with x and y intercepts ⅛ and \(\frac{1}{4√2} \) respectively and l₂ be the line in zx-plane with x and z intercepts -⅛ and \(−\frac{1}{6√3}\) respectively. If d is the shortest distance between the line l₁ and l₂, then d^–2 is equal to ______.

Answer 1

Correct Answer: 51

The correct answer is: 51.

\(\frac{x-\frac{1}{8}}{\frac{1}{8}}=\frac{y}{-\frac{1}{4\sqrt2}}=\frac{z}{0}....L_1\)

or

\(\frac{x-\frac{1}{8}}{1}=\frac{y}{-\sqrt2}=\frac{z}{0}....(i)\)

\(=\frac{\sqrt2}{\sqrt{32+16+54}}=\frac{!}{\sqrt51}\)

d^–2 = 51