How Do You Determine the Value of k in a Plane Equation?

Thread starter vorcil
Start date May 18, 2009
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Plane Point

In summary, a point is said to be contained in a plane when it satisfies the equation of the plane. To determine if a point lies on a plane, its coordinates can be substituted into the equation. The definition of a plane that contains a point requires its coordinates and the equation of the plane. A point can lie on multiple planes if they intersect at the same point. Mathematically, the relationship between a point and a plane is described by the equation of the plane, which relates the point's coordinates to the constants A, B, C, and D.

May 18, 2009

vorcil

If the plane
2x-3y+z=k
contains the point (4,2,5)
then k =

help please?

2*4 - 3*2 + 5 = k?
k=7
is that right?

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May 18, 2009

rock.freak667

Homework Helper

Yes.

May 25, 2009

Architeuthis Dux

Yes, that is correct. The equation of the plane 2x-3y+z=k can be rewritten as k=2x-3y+z. Plugging in the coordinates of the given point (4,2,5), we get k=2*4-3*2+5=8-6+5=7. Therefore, k=7.

FAQ: How Do You Determine the Value of k in a Plane Equation?

What does it mean for a plane to contain a point?

When we say that a plane contains a point, it means that the point lies on the plane, and the coordinates of the point satisfy the equation of the plane.

How can you determine if a point lies on a plane?

To determine if a point lies on a plane, you can substitute the coordinates of the point into the equation of the plane. If the equation is satisfied, then the point lies on the plane.

What information is needed to define a plane that contains a point?

To define a plane that contains a point, we need the coordinates of the point and the equations of the plane. The equation of a plane can be in the form of Ax + By + Cz + D = 0, where A, B, and C are constants and x, y, and z are variables.

Can a point lie on more than one plane?

Yes, a point can lie on more than one plane. This can happen when multiple planes intersect at the same point.

How is the relationship between a point and a plane described mathematically?

The relationship between a point and a plane is described mathematically by the equation of the plane. The equation relates the coordinates of the point to the constants A, B, C, and D, which determine the orientation and position of the plane in 3-dimensional space.