Find the equation of the plane through the point (1, 2, 3) such that it contains the line in the z = 0 plane given by x + y = 1.

Answer 1

Lets label the points here.

A ( 1, 0 , 0 ) and B ( 0, 1,0 ) the points where the line x + y = 1 intersects the x-axis and the y-axis respectively.

Let Ω( 1, 2, 3 ) be the given point .

To find the equation of the plane in question we need only one more thing, and this is the normal

vector , call in n of the plane . Let us call the unknown plane Π.

Vector AΩ =< 0, 2, 3 > and vector BΩ = < 1, 1, 3 >.

Then vector AΩ x BΩ = < 3, 3, -2 > and this vector could serve us beautifully as the n vector.

Hence the equation of plane Π is 3 (x- 0) + 3 (y - 1) - 2 z = 0