Find the scalar equation for a plane perpendicular to another plane

In summary: More information is needed to find the specific plane.In summary, to find the scalar equation of a plane that contains the point P(4,9,-3) and is perpendicular to the plane 3x - 5z + 3 = 0, we need more information as there are an infinite number of planes that meet these criteria.
  • #1
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Find the scalar equation of a plane that contains the point P(4,9,-3) and is perpendicular to the plane 3x - 5z + 3 = 0

I know that the normal vector of the given plane is 3,0,-5. I also know that in order for two planes to be perpendicular, their normal vectors must also be perpendicular. I think i should use the normal vector (3,0,-5) and the point to make a line but I don't know where to go from there.
 
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  • #2
I think you are right, you need to form a line on the new plane and find another vector,
and if you do the cross product with these two vectors, you will find the vector normal to the new plane.

you can check your answer by doing the dot product between the two normal vectors and see if you get zero.

I think this is how its done.
 
  • #3
vybear said:
Find the scalar equation of a plane that contains the point P(4,9,-3) and is perpendicular to the plane 3x - 5z + 3 = 0

I know that the normal vector of the given plane is 3,0,-5. I also know that in order for two planes to be perpendicular, their normal vectors must also be perpendicular. I think i should use the normal vector (3,0,-5) and the point to make a line but I don't know where to go from there.
Notice that the problem asks for "a plane" and not "the plane." If you think about this awhile, you should realize that there are an infinite number of planes that are perpendicular to the plane 3x - 5z + 3 = 0. There are even an infinite number of planes that pass through (4, 9, -3) that are perpendicular to the given plane.
 

1. What is a scalar equation for a plane?

A scalar equation for a plane is a mathematical representation of a plane in three-dimensional space. It is in the form of ax + by + cz = d, where a, b, and c are the coefficients of the x, y, and z variables, respectively, and d is a constant term.

2. How do you find the scalar equation for a plane?

To find the scalar equation for a plane, you need to know the normal vector of the plane. This can be determined by taking the cross product of two non-parallel vectors on the plane. Once you have the normal vector, you can plug in its components into the general form of the scalar equation (ax + by + cz = d) and solve for d by using a point on the plane.

3. What does it mean for a plane to be perpendicular to another plane?

Two planes are perpendicular to each other if they intersect at a right angle. This means that their normal vectors are also perpendicular to each other.

4. Can a plane be perpendicular to more than one plane?

Yes, a plane can be perpendicular to an infinite number of planes. This is because the normal vector of a plane can vary in direction, as long as it remains perpendicular to the normal vector of the other plane.

5. Are there any real-life applications of finding the scalar equation for a plane perpendicular to another plane?

Yes, finding the scalar equation for a plane perpendicular to another plane is useful in various fields such as engineering, physics, and computer graphics. For example, in engineering, it can be used to determine the forces acting on a surface or to calculate the normal force in a mechanical system. In computer graphics, it can be used to create 3D images and animations.

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