Vector Subtraction Calculator

Published on: February 8, 2026

This Vector Subtraction Calculator helps you subtract two 3D vectors by subtracting their corresponding components. Subtract the x-components, y-components, and z-components separately, then write the results together as a new vector. This follows the vector subtraction rule used in coordinate geometry and vector algebra. It is a simple way to check answers, understand the method clearly, and practise vector operations step by step.

Step-by-step method

  1. Identify the components of A and B.
  2. Write the component-wise subtraction rule.
  3. Substitute the components into the rule.
  4. Subtract corresponding components to get the result.

Formula:

AB=( a1b1, a2b2, a3b3 )

Example 1: (1,2,3),(4,5,6)

Step 1 - Identify the components.

In this problem: List the components of both vectors.

a1=1, a2=2, a3=3
b1=4, b2=5, b3=6

Step 2 - Write the rule.

In this problem: Subtract corresponding components.

AB=( a1b1, a2b2, a3b3 )

Step 3 - Substitute the components.

In this problem: Place your values into the rule.

AB=( 14, 25, 36 )

Step 4 - Subtract and simplify.

In this problem: Compute each component difference.

AB=( -3, -3, -3 )

Final answer: A − B = ( -3, -3, -3 )

Example 2: (5/2,0,0),(1/2,0,0)

Step 1 - Identify the components.

In this problem: List the components of both vectors.

a1=
5
2
, a2=0, a3=0
b1=
1
2
, b2=0, b3=0

Step 2 - Write the rule.

In this problem: Subtract corresponding components.

AB=( a1b1, a2b2, a3b3 )

Step 3 - Substitute the components.

In this problem: Place your values into the rule.

AB=(
5
2
1
2
, 00, 00 )

Step 4 - Subtract and simplify.

In this problem: Compute each component difference.

AB=( 2, 0, 0 )

Final answer: A − B = ( 2, 0, 0 )