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+1 vote
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in 3D Coordinate Geometry by (31.4k points)
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Show that the line \(\vec{r} = (2\hat{i}-2\hat{j}+3\hat{k}) + \lambda (\hat{i}-\hat{j}+4\hat{k}).\) is parallel to the plane \(\vec{r} . (\hat{i}+5\hat{j}+\hat{k}) = 5\) Also, find the distance between them.

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by (30.9k points)
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Best answer

As we know that the line \(\vec{r} = \vec{a} + \lambda \,\vec{b}\) is parallel to the plane \(\vec{r}.\vec{n}=q\) only when \(\vec{b}.\vec{n}=0\) and the distance between the line and the plane is given by

Hence, the given line is parallel to the given plane.

Now, distance between the given line and the given plane

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