Find the equation of the plane which passes through O and is parallel to z−(3x+4y)=2

The equation of a plane in 3D space is given by the formula Ax + By + Cz = D, where A, B, C, and D are constants, and x, y, and z are the coordinates of any point on the plane.

The given equation is z - (3x + 4y) = 2. We can rewrite this in the standard form as -3x - 4y + z = 2. Here, A = -3, B = -4, C = 1, and D = 2.

A plane that is parallel to another plane will have the same A, B, and C values, but a different D value. Since the plane passes through the origin O(0,0,0), we can find the new D value by substituting these coordinates into the equation:

-30 - 40 + 1*0 = D D = 0

So, the equation of the plane which passes through O and is parallel to z - (3x + 4y) = 2 is -3x - 4y + z = 0.