Find an equation of the plane that passes through the origin and its perpendicular to the vector [1,-2,5]

x - 2y + 5z = 0

Step-by-step explanation:

The standard equation is of the form, Ax + By + Cz = 0

The equation of the plane that passes through the origin (0, 0, 0) and is perpendicular to [1, - 2, 5] is

A = 1, B = - 2, C = 5

x = y = z = 0 (at origin)

A (x-0) + B (y-0) + C (z-0) = 0

(x - 0) - 2 (y-0) + 5 (z-0) = 0

x - 2y + 5z = 0