Direction Vector from Symmetric Equation (3D) Calculator

This Direction Vector from Symmetric Equation (3D) Calculator helps you find the direction vector of a line in three-dimensional space from its symmetric equation. Read the denominators of the symmetric form to identify the direction values, and treat any constant coordinate as having a zero component in the direction vector. This gives the vector that shows the line’s direction in x, y, and z. 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 the direction components a, b, c from the symmetric form.
2. Use d = ⟨a, b, c⟩.
3. Substitute values to write the direction vector.

Formula:

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

Step 1 - Identify the direction components.

In this problem: From the symmetric form, the direction components are a, b, c. If a coordinate is written as x = constant, then its component is 0.

Step 2 - Write the direction vector formula.

In this problem: Use d = ⟨a, b, c⟩.

Step 3 - Substitute values.

In this problem: Substitute your a, b, c values.

Final answer: d=<2,-1,4>

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

Step 1 - Identify the direction components.

In this problem: From the symmetric form, the direction components are a, b, c. If a coordinate is written as x = constant, then its component is 0.

Step 2 - Write the direction vector formula.

In this problem: Use d = ⟨a, b, c⟩.

Step 3 - Substitute values.

In this problem: Substitute your a, b, c values.

Final answer: d=<0,3,-4>