Vector Subtraction Calculator

How to Calculate Vector Subtraction

Vector subtraction is a fundamental operation in vector mathematics. It involves finding the difference between two vectors. This guide will explain how to perform vector subtraction step by step.

Vector Subtraction Formula

For vectors \(\vec{a} = (a_1, a_2, ..., a_n)\) and \(\vec{b} = (b_1, b_2, ..., b_n)\), the subtraction \(\vec{a} - \vec{b}\) is defined as:

\(\vec{a} - \vec{b} = (a_1 - b_1, a_2 - b_2, ..., a_n - b_n)\)

Where:

• \(a_i\) is the i-th component of vector \(\vec{a}\)
• \(b_i\) is the i-th component of vector \(\vec{b}\)

Calculation Steps

1. Identify the components of both vectors.
2. Subtract the corresponding components of vector \(\vec{b}\) from vector \(\vec{a}\).
3. Write the result as a new vector with the calculated differences as its components.

Example Calculation

Let's subtract \(\vec{b} = (1, 2, 3)\) from \(\vec{a} = (4, 5, 6)\):

Step 1: Identify the components

\(\vec{a} = (4, 5, 6)\)

\(\vec{b} = (1, 2, 3)\)

Step 2: Subtract corresponding components

First component: 4 - 1 = 3

Second component: 5 - 2 = 3

Third component: 6 - 3 = 3

Step 3: Write the result

\(\vec{a} - \vec{b} = (3, 3, 3)\)

Visual Representation

This diagram illustrates vector subtraction in 2D space. The blue arrow represents vector \(\vec{a}\), the red arrow represents vector \(\vec{b}\), and the green arrow shows the resulting vector \(\vec{a} - \vec{b}\).