Find a Cartesian equation for the plane P in R3 that passes through the points A(1,0,0), B(0,3,0) and C(0,0,4).

I there any way to do this question without using the cross product?

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- September 20th 2010, 11:34 AMSyNtHeSiSEquation of plane
Find a Cartesian equation for the plane P in R3 that passes through the points A(1,0,0), B(0,3,0) and C(0,0,4).

I there any way to do this question without using the cross product? - September 20th 2010, 01:48 PMemakarov
See this Wikipedia article, especially Method 2. It uses matrix algebra to solve a system of linear equations, but this system can be solved using any method, such as the elimination of variables, which I believe is taught in school. You could put d = -1 (or any other non-zero number).

- September 20th 2010, 08:06 PMSoroban
Hello, SyNtHeSiS!

Quote:

The general equation of a plane is: .

Substitute the three given points:

So we have: .

Multiply through by

- September 21st 2010, 12:57 AMMathoMan
Form vectors and . Now you have one point (A with its radius vector ) and two vectors that lie in the same plane. Using them you can form a parametric equation of that plane, describing a radius vector of an arbitrary point in that plane.

Componentwise it looks like this.

And from there it is easy to form the equation of the plane, just substituting and in the first equation with the expression from second and third eq.

There you have it mate.