Question

Find an equation of the plane with x-intercept a, y-intercept b, and z-intercept c.

a) x/a + y/b + z/c = 1
b) a/x + b/y + c/z = 1
c) ax + by + cz = 1
d) 1/a + 1/b + 1/c = 1

Answer 1

The correct equation for a plane with x-intercept a, y-intercept b, and z-intercept c is x/a + y/b + z/c = 1.

Step-by-step explanation:

The equation of the plane with x-intercept a, y-intercept b, and z-intercept c can be represented as x/a + y/b + z/c = 1. This equation is derived by understanding that a plane that crosses the x-axis at 'a', the y-axis at 'b', and the z-axis at 'c' will have the given point (a, 0, 0), (0, b, 0), and (0, 0, c) respectively. When we normalize these points by their intercepts and sum them up to equal one, it indicates that any point (x, y, z) on this plane will satisfy this equation.