Question

The shortest distance between the lines whose equations are $\overset{\rightarrow}{r}$= t($\widehat{i}$ + $\widehat{j}$+ $\widehat{k}$) and $\overset{\rightarrow}{r}$ = $\widehat{k}$ + s ($\widehat{i}$ – 2$\widehat{j}$ + 3$\widehat{k}$) is :

• A. 3
• B. $\frac{3}{\sqrt{38}}$
• C. $\frac{\sqrt{3}}{14}$
• D. $\frac{2}{\sqrt{13}}$

Answer 1

Answer: (B)

$\frac{3}{\sqrt{38}}$

Answer 2

Shortest distance between two lines is given by

= $\left| \frac{(\widehat{i} + \widehat{j} + \widehat{k}) \times (\widehat{i}–2\widehat{j} + 3\widehat{k})}{(\widehat{i} + \widehat{j} + \widehat{k}) \times (\widehat{i}–2\widehat{j} + 3\widehat{k})}\widehat{k} \right|$

= $\left| \frac{(5\widehat{i}–2\widehat{j}–3\widehat{k})}{\sqrt{25 + 4 + 9}}\widehat{k} \right|$

= $\frac{3}{\sqrt{38}}$