The foot of the perpendicular drawn from the origin to a plane is (2, 1, 5). Find the equation of the plane.

Asked by Topperlearning User | 4th Jun, 2014, 01:23: PM

Expert Answer:

Since, the foot of the perpendicular to the plane is A(2, 1, 5). Therefore, (2, 1, 5) is the point on the plane.

So, equation of the plane passing through the point (2,.1, 5) is:
a(x – 2) + b(y – 1) + c(z – 5) = 0.
Now, the direction ratios of the perpendicular line OA = 2 – 0, 1 – 0, 5 – 0, i.e., 2, 1, 5.
 
Therefore, the required plane is:
2(x – 2) + 1(y – 1) + 5(z – 5) = 0
i.e, 2x + y + 5z = 30.
 
 

Answered by  | 4th Jun, 2014, 03:23: PM