The shortest distance between the lines \(\vec{r}=\left(\frac{1}{3}\overset{^}{i}+2\overset{^}{j}+\frac{8}{3}\overset{^}{k}\right)+\lambda (2\overset{^}{i}-5\overset{^}{j}+6\overset{^}{k})\) and \(\vec{r}=\left(-\frac{2}{3}\overset{^}{i}-\frac{1}{3}\overset{^}{k}\right)+\mu (\overset{^}{j}-\overset{^}{k}),\lambda ,\mu \in R\), is:

[JEE Main 2026, 4 Apr (Shift 2)]

Question

The shortest distance between the lines \(\vec{r}=\left(\frac{1}{3}\overset{^}{i}+2\overset{^}{j}+\frac{8}{3}\overset{^}{k}\right)+\lambda (2\overset{^}{i}-5\overset{^}{j}+6\overset{^}{k})\) and \(\vec{r}=\left(-\frac{2}{3}\overset{^}{i}-\frac{1}{3}\overset{^}{k}\right)+\mu (\overset{^}{j}-\overset{^}{k}),\lambda ,\mu \in R\), is:

[JEE Main 2026, 4 Apr (Shift 2)]

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The shortest distance between the lines \(\vec{r}=\left(\frac{1}{3}\overset{^}{i}+2\overset{^}{j}+\frac{8}{3}\overset{^}…

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