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Show that the lines vectors =(3i  -15j + 9k) + λ(2i - 7j + 5k), and r = (-i + j + 9k) + μ (2i + j - 3k) do not intersect.

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Best answer

Given equations :

3. Shortest distance between two lines :

The shortest distance between the skew lines 

 The shortest distance between the skew lines \(\vec r=\bar a_1+\lambda \bar{b_1}\) and

\(\vec r=\bar a_2+\lambda \bar {b_2}\) is given by,

For given lines,

= - 68 + 256 + 0

= 188

Therefore, the shortest distance between the given lines is

As d ≠ 0

Hence, the given lines do not intersect.

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