Please help me on this question.

Question

Write plane equation that passes A(1,-2,6) B(5,-4,-2) points and intersects Ox and Oy equally.

 

Answer 1

The equation of a plane in 3d space can be written as 

 

α x +  β y + γ z = 1        for some value of the parameters α, β, γ

 

The fact that point A is in this plane means that

 

α - 2 β + 6 γ =1       and the fact that  point  B us in the plane means that

 

5 α - 4 β - 2 γ =1

 

The fact that the plane intercepts the x and y axes at the same value means that α = β

 

This gives three equations for the three unknowns (α, β, γ).

 

The system can be solved by standard techniques.  For example if the second equation is multiplied by 3 and added to the first equation   one gets   16 α - 14 β = 4.    This combined with α = β  leads to α = 2,  β = 2.

Either of the first two equations then leads to γ = 1/2.      The equation of the plane is therefore

 

2 x + 2 y + (1/2) z = 1