4x-2y+4z, write an equation of the plan, having the give x,y,&z intercepts.?

Question

I dont understand how to find the points, then how i would plot 3 numbers on a graph.

Answer 1

Your question is somewhat confuse. 4x-2y+4z is not an equation... it is missing the "=" signal and the other member.

1) You may use the formula a(x-x1) + b(y-y1) + c(z-z1) =0 where (x1,y1,z1) are a point of the plane and (a,b,c) a perpendicular vector.
For example: if the intercepts are P(3,0,0), Q(0,4,0) and R(0,0,5)
you find the vector PQ= Q-P and PR = P-R and use the vector product to get the vector (a,b,c) the use the formula.
This proceeding can be used for whatever three givens points.

2)When the points are the intercepts, there is a particular way:
You may use the formula: ax + by + cz + d =0

To find the perpendicular vector you just do:(same example) intercepts: (3,0,0), (0,4,0) and (0,0,5)
a= 4x5 b=3x5 c= 3x4 and d=3x4x5... did you get?( the component a(of x) is the product of the intercepts with y and z... and so forth... the d is the product of the three numbers)