Show that the line is parallel to the plane

Question

Philoid · Accepted Answer

Given :

Equation of plane : :

Equation of line :

To Prove : Given line is parallel to the given plane.

Answer :

Comparing given plane i.e.

with , we get,

This is the vector perpendicular to the given plane.

Now, comparing given equation of line i.e.

with , we get,

Now,

= 20 – 8 – 12

= 0

Therefore, vector normal to the plane is perpendicular to the vector parallel to the line.

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