Thread: Planes

Originally Posted by Question

The plane 'H'passes through the points

A(-1, -1, 1), B(4, 2, 1) and C (2, 1, 0).

(a) Find a vector equation of the line perpendicular to 'H' which passes through the point D (1, 2, 3).

(b) The perpendicular from D to the plane 'H' meets 'H' at the point E. Find the coordinates of E.

I understand part(a) but struggling with part(b). Can I have help? Thanks in advance.

Originally Posted by Air

I understand part(a) but struggling with part(b). Can I have help? Thanks in advance.

One approach:

1. Get the Cartesian equation of the plane H: ax + by +cz = d.

2. Get a parametric equation of the line found in (a): x = x(t), y = y(t), z = z(t).

3. Substitute x = x(t), y = y(t), z = z(t) into ax + by +cz = d and solve for t.

4. Substitute the value of t into x = x(t), y = y(t), z = z(t). These are the required coordinates of E.