Question:medium
The shortest distance between the lines $\vec{r}=\hat{i}+\hat{j}+3\hat{k}+\lambda(2\hat{i}+2\hat{j}+\hat{k})$ and $\vec{r}=(2\mu+1)\hat{i}+(2\mu-1)\hat{j}+(\mu+1)\hat{k}$ where $\lambda$ and $\mu$ are parameters, is
The shortest distance between the lines $\vec{r}=\hat{i}+\hat{j}+3\hat{k}+\lambda(2\hat{i}+2\hat{j}+\hat{k})$ and $\vec{r}=(2\mu+1)\hat{i}+(2\mu-1)\hat{j}+(\mu+1)\hat{k}$ where $\lambda$ and $\mu$ are parameters, is
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Logic Tip: Always quickly inspect the direction vectors before diving into the skew lines formula (the one with the determinant scalar triple product). If the lines are parallel, the scalar triple product will be zero, and you must use the parallel line distance formula instead.
Updated On: Apr 27, 2026
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