Question:medium
The shortest distance between the straight line
\[
\vec{r}
= 3\hat{i}+12\hat{j}+5\hat{k}
+\lambda(2\hat{i}),
\qquad \lambda\in\mathbb{R},
\]
and the \(x\)-axis is:
The shortest distance between the straight line
\[
\vec{r}
= 3\hat{i}+12\hat{j}+5\hat{k}
+\lambda(2\hat{i}),
\qquad \lambda\in\mathbb{R},
\]
and the \(x\)-axis is:
Show Hint
When a line's direction vector is \((1, 0, 0)\), the line is horizontal (parallel to x-axis). The shortest distance to the x-axis is simply the Euclidean distance of its y and z coordinates from the origin in the YZ-plane.
Updated On: Jun 25, 2026
- 7
- 12
- \(3\sqrt{5}\)
- \(5\sqrt{3}\)
- 13
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The Correct Option is
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