Question

Find whether the plane 5x-2y-12z+47=0 contains the line x-1/6=y+2/3=z-4/2 or not

Answer 1

Answer:

Yes, Given Plane contains the given line

Step-by-step explanation:

Hi,

Given equation of thee plane is P: 5x-2y-12z+47=0

Direction ratios of the normal to the plane are ( 5, -2, -12)

Given equation of the  x-1/6=y-2/3=z-4/2

This means the line is passing through the point A(1, 2, 4) and

having its direction ratios (6, 3, 2)

If the line has to be contained in the plane, the point on the line

should lie on the plane and the normal to the plane should be

also perpendicular to the contained line.

Substituting A(1,2,4) in plane P: 5x-2y-12z+47 = 0, we observe

that 5(1) -2(2) -12(4) + 47 = 0.

If we consider the dot product of dr's of normal to the plane and

dr's of the line , we observe that 5(6) -2(3) -12(2) = 0

hence, normal to the plane is perpendicular to the given line,

Hence, the plane contains the given line.

Hence point A lies on the given plane.

Hope it helps !