What is the equation of the plane passing through the point (1, 2, 3) with norma
Practice Questions
Q1
What is the equation of the plane passing through the point (1, 2, 3) with normal vector (1, -1, 1)? (2023)
x - y + z = 0
x + y + z = 6
x - y + z = 1
x + y - z = 0
Questions & Step-by-Step Solutions
What is the equation of the plane passing through the point (1, 2, 3) with normal vector (1, -1, 1)? (2023)
Step 1: Identify the point through which the plane passes. This point is (1, 2, 3).
Step 2: Identify the normal vector of the plane. The normal vector is (1, -1, 1).
Step 3: Use the point-normal form of the equation of a plane, which is given by: a(x - x0) + b(y - y0) + c(z - z0) = 0, where (x0, y0, z0) is the point and (a, b, c) are the components of the normal vector.
Step 4: Substitute the values into the equation. Here, a = 1, b = -1, c = 1, and (x0, y0, z0) = (1, 2, 3).
