Plane Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

hard
Does the point (2,3,โˆ’1)(2, 3, -1) lie on the plane 2xโˆ’y+3z=42x - y + 3z = 4?

Solution

  1. 1
    Step 1: Substitute the point into the plane equation: 2(2)โˆ’(3)+3(โˆ’1)2(2) - (3) + 3(-1).
  2. 2
    Step 2: Calculate: 4โˆ’3โˆ’3=โˆ’24 - 3 - 3 = -2.
  3. 3
    Step 3: Since โˆ’2โ‰ 4-2 \neq 4, the point does not satisfy the equation.

Answer

No, (2,3,โˆ’1)(2,3,-1) does not lie on the plane 2xโˆ’y+3z=42x - y + 3z = 4.
A point lies on a plane if and only if its coordinates satisfy the plane's equation. Substituting and checking is the straightforward test. The point (2,3,โˆ’1)(2,3,-1) gives a left-hand side of โˆ’2-2, not 44, so it is off the plane.

About Plane

A perfectly flat surface extending infinitely in all directions with zero thickness; defined by three non-collinear points.

Learn more about Plane โ†’

More Plane Examples

Example 1 easy

What is the equation of the xy-plane in 3D space?

Example 2 medium

Three points A[formula], B[formula], C[formula] lie on a plane. Write the equation of that plane.

Example 3 easy

How many dimensions does a plane have, and how many coordinates are needed to specify a point on a p

โ† All Plane Examples Plane Concept

Related Concepts

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