Table of Contents

## How do you find the equation of a line using parametric equations?

By writing the vector equation of the line in terms of components, we obtain the parametric equations of the line, x = x0 + at, y = y0 + bt, z = z0 + ct. The components a, b and c of are called the direction numbers of the line. Let 0 = 1,2,0 and = 1,3,2.

## What is Equation of plane in normal form?

The normal form of a plane is Ax+By+Cz=D, where A2+B2+C2=1 and D≥0. For the point (x,y,z), the dot product (A,B,C,D). (x,y,z,1) gives the distance from the plane to the point, so that distance 0 means the point is on the plane.

**How do you find the equation of the plane?**

If P is any other point in the plane and r_0and rare the position vectors of the points P_0 and P, respectively, then an equation of the plane is since each vector in the plane must be orthogonal to the normal vector nand the vector r-r_0is a vector in the plane.

**What is the equation of the plane -2x-3y+Z=2?**

As with equations of lines in three dimensions, it should be noted that there is not a unique equation for a given plane. The graph of the plane -2x-3y+z=2 is shown with its normal vector. Example Find an equation of the plane passing through the points P(1,-1,3), Q(4,1,-2), and R(-1,-1,1).

### What are the parametric equations of a line in three dimensions?

Thus, the line has vector equation r=<-1,2,3>+t<3,0,-1>. Hence, the parametric equations of the line are x=-1+3t, y=2, and z=3-t. It is important to note that the equation of a line in three dimensions is not unique.

### How do you find the scalar equation of a plane?

Start with the first form of the vector equation and write down a vector for the difference. This is called the scalar equation of plane. Often this will be written as, where d =ax0 +by0 +cz0 d = a x 0 + b y 0 + c z 0. This second form is often how we are given equations of planes.