Show that the line is parallel to the plane

Question

Philoid · Accepted Answer

Given :

Equation of plane : :

Equation of a line :

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

Comparing given plane i.e.

with , we get,

This is the vector perpendicular to the given plane.

Now, comparing the given the equation of line i.e.

with , we get,

Now,

= 1 – 5 + 4

= 0

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

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