Question

How is the line $\frac{x-4}{4}=\frac{y-12}{12}=\frac{z-8}{8}$ related to the planes
(A) $x-y+z=0$
(B) $x-y+z-6=0$

• A. parallel to plane A but not B
• B. parallel to plane A and also lies in plane A but not parallel to B
• C. parallel to plane A and also lies in plane A
• D. none of these

Answer 1

The correct option is C parallel to plane A and also lies in plane A

A line is inclined at Φ to a plane. The vector equation of the line is given by

$\overrightarrow{r}=\overrightarrow{a}+\lambda \overrightarrow{b}$

Let $\theta$ be the angle between the line and the normal to the plane. Its value can be given by the following equation

$cos\theta =|\frac{\overrightarrow{b}.\overrightarrow{n}}{|\overrightarrow{b}|.|\overrightarrow{n}|}|$

Finding the value of the $\Phi$ between the line and the plane we know that

parallel to plane A and also lies in plane A.