Find the equation of the plane passing through the point (1,2,1) and perpendicular to the line joining the points (1,4,2) and (2,3,5). Find also the perpendicular distance of the origin from this plane.

Question

Philoid · Accepted Answer

We know that the vector equation of the plane passing through a point and normal to is

……(i)

Here,

And,

Putting the value of andin (i)

.

……(ii)

Dividing (ii) by

So the perpendicular distance of plane from origin = units

Equation of plane:

Equation of plane : x – y + 3z – 2 = 0.