- #1
Mathematicsss
Homework Statement
Why is that we can set two variables zero in an equation of a plane to find a point on that plane? What is the proof for this?
The equation of a plane in Calculus 3 is represented in the form Ax + By + Cz + D = 0, where A, B, and C are the coefficients of the x, y, and z variables, respectively.
To find the equation of a plane using three points, you can use the formula (x - x1)(y2 - y1) - (x2 - x1)(y - y1) = (x - x1)(z2 - z1) - (x2 - x1)(z - z1) = (y - y1)(z2 - z1) - (y2 - y1)(z - z1) = 0, where (x1, y1, z1), (x2, y2, z2), and (x3, y3, z3) are the three points on the plane.
The general form of the equation of a plane is Ax + By + Cz + D = 0, where A, B, and C are the coefficients of the x, y, and z variables, respectively.
To find a point on a plane in Calculus 3, you can use the formula d = |Ax1 + By1 + Cz1 + D| / √(A2 + B2 + C2), where d is the distance from the point (x1, y1, z1) to the plane.
Yes, the equation of a plane can be written in different forms, such as normal form and vector form. However, the general form (Ax + By + Cz + D = 0) is the most commonly used form in Calculus 3.