Show that the line \vec{r}=(2\hat{i}+5\hat{j}+7\hat{k})+\lambda(\h | Filo
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Class 12

Math

3D Geometry

Three Dimensional Geometry

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Show that the line is parallel to the plane . Also, find the distance between them.

Solution:
We know that a line is parallel to the plane only when 
this line is perpendicular to the normal to the plane.

So, we must have
Here,
Hence, the given line is parallel to the given plane.

Required distance between the line and the plane

units.
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