How Do You Find a Scalar Equation for a Plane Through Three Points?

In summary, the conversation discusses finding a scalar equation that passes through three given points. The speaker initially tries to use the vector equation form but realizes that there is an error in their calculation. They then mention using matrix algebra as a better approach to solving the problem. The concept of an equation passing through points is also questioned.
  • #1
Hollysmoke
185
0
The question is,

Find a scalar equation that passes through the points (3,2,3), (-4,1,2) and (-1,3,2).

What I did was put that into the vector equation form, using (3,2,3) as a position vector, resulting in:

r=(3,2,3) +t(-7,-1,-1) + s(-5,2,0)

Then I found the cross product of the directional vectors and went from there, but my final answer was different then the one in the textbook. Can someone tell me what I did wrong please?
 
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  • #2
s should be multiplied by (-3, 2, 0). Looks like you added instead of subtracted.

The better way to do this problem is to solve the system of equations, with matrix algebra if you have it.
 
  • #3
I have no idea what it means for an "equation" to pass through three points. A line or a plane can pass through points but an equation is not a geometric object and has nothing to do with "points".
 

Related to How Do You Find a Scalar Equation for a Plane Through Three Points?

1. What is a scalar equation in geometry?

A scalar equation in geometry is a mathematical equation that only involves scalar quantities, which are quantities that have only magnitude and no direction. In other words, a scalar equation does not involve any vectors or directional information.

2. How is a scalar equation different from a vector equation?

A vector equation involves both magnitude and direction, whereas a scalar equation only involves magnitude. Additionally, a vector equation can represent multiple solutions, while a scalar equation typically represents a single solution.

3. What are some common examples of scalar equations in geometry?

Some common examples of scalar equations in geometry include the Pythagorean theorem, the distance formula, and the slope formula. These equations only involve magnitude and do not involve any directional information.

4. How is a scalar equation used in real life?

Scalar equations are used in many real-life applications, such as calculating distances, areas, and volumes. For example, the distance formula can be used to calculate the distance between two points on a map, and the Pythagorean theorem can be used to find the length of the hypotenuse of a right triangle.

5. Can a scalar equation be used in three-dimensional geometry?

Yes, a scalar equation can be used in three-dimensional geometry. However, it will typically involve three variables and represent a plane rather than a line. Examples of three-dimensional scalar equations include the equation of a sphere or the equation of a plane in three-dimensional space.

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