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

In summary, to 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), you need to determine the displacement vector between the two given points and cross it with <1, 0, 0> to find a normal vector to the plane. Then, you can use this normal vector and one of the given points to determine the general form of the equation of the plane.
  • #1
plutolover
4
0
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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  • #2
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.
 

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

1. What is the difference between a line and a plane?

A line is a one-dimensional object that extends infinitely in both directions, while a plane is a two-dimensional object that extends infinitely in all directions. In other words, a line has no width or depth, while a plane has both width and depth.

2. How are lines and planes represented mathematically?

A line can be represented by an equation in the form y = mx + b, where m is the slope and b is the y-intercept. A plane can be represented by an equation in the form Ax + By + Cz + D = 0, where A, B, and C are the coefficients of the x, y, and z variables, and D is a constant term.

3. How many points are needed to uniquely define a line?

Two points are needed to uniquely define a line. This is because any two distinct points will determine a unique line that passes through both of them.

4. Can a line and a plane intersect at more than one point?

No, a line and a plane can only intersect at one point. This is because a line is a one-dimensional object while a plane is a two-dimensional object, so they cannot share more than one point in common.

5. What is the shortest distance between a point and a plane?

The shortest distance between a point and a plane is the length of the perpendicular line that connects the point to the plane. This can be calculated using the formula d = |Ax + By + Cz + D| / √(A^2 + B^2 + C^2), where (x, y, z) is the coordinates of the point and A, B, C, and D are the coefficients of the plane equation.

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