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

Question

Philoid · Accepted Answer

We know that line and plane is parallel if

……(1)

Given, the equation of the line
and equation of plane is the

,

So, and

Now,

=

= 1 + 3 – 4 = 0

So, the line and the plane are parallel

We know that the distance (D) of a plane from a point is given by

We take the mod value

So,