# Resultant Vector Calculator

Vectors are quantities with both magnitude and direction. Vectors help to simultaneously represent different quantities in the same expression.

## What is a Resultant Vector Calculator?

'**Resultant Vector Calculator**' is an online tool that helps to calculate the resultant value for a given vector. Online Resultant Vector Calculator helps you to calculate the resultant value for a given vector within a few seconds.

### Resultant Vector Calculator

**NOTE:** Enter the numbers only up to two digits.

## How to Use Resultant Vector Calculator?

Please follow the steps below on how to use the calculator:

**Step 1:**Enter coefficients of two vectors in the given input boxes.**Step 2:**Click on the "**Add**" button to calculate the resultant value for a given vector**Step 3:**Click on the "**Reset**" button to clear the fields and enter the new values.

## How to Find Resultant Vector?

A resultant vector is defined as a vector that gives the combined effect of all the vectors. When we add two or more vectors, the outcome is the resultant vector. Let \(\overrightarrow{A} = x\hat i + y \hat j +z\hat k\) and \(\overrightarrow{B} = p\hat i + q \hat j +r\hat k\). The resultant vector is calculated using the formula:

**Resultant vector = \(\overrightarrow{A} +\overrightarrow{B} = (x + p)\hat i + (y + q) \hat j +(z + r)\hat k\)**

Where x, y, z, p, q, and r are numeric values and \( \hat i , \hat j ,\hat k\) are the unit vectors along the x-axis, y-axis, and z-axis respectively.

Let's see an example to understand briefly.

**Solved Examples on Resultant Vector Calculator**

**Example 1:**

Find the resultant of two given vectors a = 4i + 2j - 5k and b = 3i - 2j + k ?

**Solution:**

Given a = 4i + 2j - 5k and b = 3i - 2j + k

Resultant = a + b = (4i + 2j - 5k) + (3i - 2j + k)

= (4 + 3)i + (2 - 2)j + (-5 + 1)k

= 7i + 0j - 4k

= 7i - 4k

Therefore, the resultant of two vectors is 7i - 4k

**Example 2:**

Find the resultant of two given vectors a = i + 3j - 4k and b = i - 7j + 3k ?

**Solution:**

Given a = i + 3j - 4k and b = i - 7j + 3k

Resultant = a + b = (i + 3j - 4k) + (i - 7j + 3k)

= (1 + 1)i + (3 - 7)j + (-4 + 3)k

= 2i - 4j - k

Therefore, the resultant of two vectors is 2i - 4j - k

**Example 3:**

Find the resultant of two given vectors a = i - 3j + 7k and b = -5i + 8j + 3k ?

**Solution:**

Given a = i - 3j + 7k and b = -5i + 8j + 3k

Resultant = a + b = (i - 3j + 7k) + (-5i + 8j + 3k)

= (1 - 5)i + (-3 + 8)j + (7 + 3)k

= -4i + 5j + 10k

Therefore, the resultant of two vectors is -4i + 5j + 10k

Similarly, you can use the calculator to find the resultant of two vectors for the following:

- a = 4i + 2j - 5k and b = -1i + 4j - 3k
- a = -2i - 5k and b = -7i + j + k

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