Question

Find the shortest distance between the lines L₁ and L₂ whose vector equations are r = (i + 2j - 4k) + λ(2i + 3j + 6k) and r = (3i + 3j - 5k) + μ(2i + 3j + 6k).

HINT: The given lines are parallel.

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CORRECT ANSWER

Answer 1

Given equations :

3. Shortest distance between two lines :

The shortest distance between the skew lines \(\vec r=\bar a_1+\lambda \bar{b}\) and

\(\vec r=\bar a_2+\lambda \bar {b}\) is given by,

For given lines,

\(=\sqrt{293}\)

Therefore, the shortest distance between the given lines is