How Do You Find the Equation of a Plane Perpendicular to the YZ-Plane?

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SUMMARY

The equation of a plane perpendicular to the YZ-plane and passing through the points (0,2,4) and (-1,-2,0) can be determined using the normal vector <1,0,0>. The displacement vector between the two points is calculated, and the cross product with <1,0,0> yields the normal vector for the plane. The general form of the equation can be expressed as x = d, where d is the x-coordinate of any point on the plane.

PREREQUISITES
  • Understanding of vector mathematics
  • Familiarity with the concept of normal vectors
  • Knowledge of cross product operations
  • Basic understanding of the equation of a plane in three-dimensional space
NEXT STEPS
  • Study vector operations, particularly the cross product
  • Learn how to derive the equation of a plane from a normal vector
  • Explore the geometric interpretation of planes in three-dimensional space
  • Practice problems involving planes and their equations in various orientations
USEFUL FOR

Students and professionals in mathematics, physics, and engineering who are working with three-dimensional geometry and need to understand the properties of planes and vectors.

plutolover
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find the general form of the equation of the plane with the given characteristics:

passes through (0,2,4) and (-1,-2,0) and is perpendicular to yz-plane


I know what the general form of an equation is, but I was wondering, do I set the direction vector to be <0,1,1> or <1,0,0>? How do I use this to determine the general form of the equation?

I started by determining the vector given by the two points and then used this vector with the cross product of the two vectors mentioned above, but I am not sure what to do after that?...
 
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plutolover said:
find the general form of the equation of the plane with the given characteristics:

passes through (0,2,4) and (-1,-2,0) and is perpendicular to yz-plane


I know what the general form of an equation is, but I was wondering, do I set the direction vector to be <0,1,1> or <1,0,0>? How do I use this to determine the general form of the equation?
The displacement vector between your two given points can be crossed with <1, 0, 0> to produce a vector that is normal to your plane.
plutolover said:
I started by determining the vector given by the two points and then used this vector with the cross product of the two vectors mentioned above, but I am not sure what to do after that?...

When you post a problem, don't delete the template elements. They are there for a reason.
 

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