Parametric Equations from Symmetric Form (3D) Calculator

This Parametric Equations from Symmetric Form (3D) Calculator helps you convert a line equation in symmetric form into parametric equations in three-dimensional space. Identify the point on the line and the direction values from the symmetric equation, then use them to write separate equations for x, y, and z in terms of a parameter. This gives the line in an easier form to work with. It is a simple way to check answers, understand the method clearly, and practise 3D coordinate geometry step by step.

Step-by-step method

1. Identify x₀, y₀, z₀ and a, b, c from the symmetric form.
2. Write the parametric equations.
3. Substitute values.

Formula:

Example 1: (x-1)/2=(y+3)/-1=z/4

Step 1 - Identify the components.

In this problem: Read off x₀, y₀, z₀ and a, b, c from the symmetric form.

Step 2 - Write the parametric equations.

In this problem: Use x = x₀ + at, y = y₀ + bt, z = z₀ + ct.

Step 3 - Substitute values.

In this problem: Substitute x₀, y₀, z₀ and a, b, c.

Final answer: x=2*t + 1, y=-t - 3, z=4*t

Example 2: (x-1/2)/3=(y+1)/2=(z-5)/(-4)

Step 1 - Identify the components.

In this problem: Read off x₀, y₀, z₀ and a, b, c from the symmetric form.

Step 2 - Write the parametric equations.

In this problem: Use x = x₀ + at, y = y₀ + bt, z = z₀ + ct.

Step 3 - Substitute values.

In this problem: Substitute x₀, y₀, z₀ and a, b, c.

Final answer: x=3*t + 1/2, y=2*t - 1, z=5 - 4*t