Question

Shortest distance between lines

$\overrightarrow{r} = 6\widehat{i} + 2\widehat{j} + 2\widehat{k} + \lambda(\widehat{i}–2\widehat{j} + 2\widehat{k})$ and$\overrightarrow{r} = –4\widehat{i}–\widehat{k} + µ(3\widehat{i}–2\widehat{j}–2\widehat{k})$ is -

• A. 0
• B.
  • 2 units
• C.
  • 30 units
• D. 9 units

Answer 1

Answer: (D)

9 units

Answer 2

Shortest Distance = $\left| \frac{\left( {\overrightarrow{a}}_{2}–{\overrightarrow{a}}_{1} \right).\left( {\overrightarrow{b}}_{1} \times {\overrightarrow{b}}_{2} \right)}{\left| {\overrightarrow{b}}_{1} \times {\overrightarrow{b}}_{2} \right|} \right|$