Adding Vectors Calculator

Vector addition is the operation of adding two or more vectors together into a vector sum.

What is Adding Vectors Calculator?

'Cuemath's Adding Vectors Calculator' is an online tool that helps to calculate the sum of two vectors. Cuemath's online Adding Vectors Calculator helps you to calculate the sum of two vectors in a few seconds.

How to Use Adding Vectors Calculator?

Please follow the below steps to calculate the sum of two vectors:

• Step 1: Enter the coefficients of two vectors in the given input boxes.
• Step 2: Click on the "Calculate" button to calculate the sum of two vectors.
• Step 3: Click on the "Reset" button to clear the fields and enter the different values.

How to Find Adding Vectors Calculator?

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

The standard form of representation of a vector is:

A₁ = a₁i^ + b₁j^ + c₁k^

A₂ = a₂i^ + b₂j^ + c₂k^

A1 + A2 = (a₁+a₂)i^ + (b₁ + b₂)j^ + (c₁ + c₂)k^

Where a₁, b₁, c_1, and a2, b₂, c₂are numeric values, and i^, j^, k^ are the unit vectors along the x-axis, y-axis, and z-axis respectively.

Solved Example:

Find the sum of two vectors a = 4i + 2j – 5k and b = 3i – 2j + k ?

Solution:

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

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

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

= 7i + 0j - 4k

= 7i - 4k

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

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

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