# Is there a symmetric form for the equation of a plane?

## Is there a symmetric form for the equation of a plane?

The symmetric form of the equation of a line is an equation that presents the two variables x and y in relationship to the x-intercept a and the y-intercept b of this line represented in a Cartesian plane. The symmetric form is presented like this: xa+yb=1, where a and b are non-zero.

How do you find the equation of two planes?

The intersection of two planes is always a line

1. r = r 0 + t v r=r_0+tv r=r0​+tv.
2. x = a x=a x=a, y = b y=b y=b, and z = c z=c z=c.
3. where a, b and c are the coefficients from the vector equation r = a i + b j + c k r=a\bold i+b\bold j+c\bold k r=ai+bj+ck.

### How do you know if two parametric lines are parallel?

we can choose two points on each line (depending on how the lines and equations are presented), then for each pair of points, subtract the coordinates to get the displacement vector. If the two displacement or direction vectors are multiples of each other, the lines were parallel.

What is the scalar equation of a plane?

The scalar equation of a plane, with normal vector n = (A, B, C), is Ax + By + Cz + D = 0.

## What is the intersection of two lines called?

Meaning of Intersection of Two Lines When two lines share exactly one common point, they are called the intersecting lines. The intersecting lines share a common point. And, this common point that exists on all intersecting lines is called the point of intersection.

What is the vector equation of a plane?

Vectors b and c are any vectors in the plane (but not parallel to each other). r is a position vector to a general point on the plane. ► The equation of the plane can then be written by: r = a + λb + µc where λ and µ take all values to give all positions on the plane.

### Can 2 planes intersect?

The intersection of two planes is a line. They cannot intersect at only one point because planes are infinite. Furthermore, they cannot intersect over more than one line because planes are flat.

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