Vector addition is all about adding two or more vectors to get a resultant vector. If x and y are two vectors given by $\vec{x}$ = a $\hat{i}$ + b $\hat{j}$ + c $\hat{k}$ and $\vec{y}$ = d $\hat{i}$ + e $\hat{j}$ + f $\hat{k}$.

Then the sum of the vectors z is given by
Where i, j and k are the components whose magnitude are added separately to get the resultant of $\vec{x}$ and $\vec{y}$.

The vector addition calculator is an amazing online tool which performs vector addition operation for given two vectors and gives answer instantly. Provided are the blocks for vectors x and y where you are supposed to put the vector component value for the given vectors.

Step 1 : Read the given problem and note down the two vectors

$\vec{x}$ = a $\hat{i}$ + b $\hat{j}$ + c $\hat{k}$

$\vec{y}$ = d $\hat{i}$ + e $\hat{j}$ + f $\hat{k}$.

Step 2 : The vector addition is given by

$\vec{x} + \vec{y} = (a + d) \hat{i} + (b + e) \hat{j} + (c + f) \hat{k}$

Add magnitude of the components of given vectors separately as above to get the resultant vector.

Below are given some problems based on vector addition which may be helpful for you.

Solved Examples

Question 1: Find vector addition if $\vec{x}$ = 2i + 3j + 5k and $\vec{y}$ = i + 2j + 7k.
Solution:

Given: $\vec{x}$ = 2i + 3j + 5k and $\vec{y}$ = i + 2j + 7k
$\vec{x}$ + $\vec{y}$ = (2 + 1) i + (3 + 2) j + (5 + 7) k
= 3i + 5j + 12k.

Question 2: Find vector addition if $\vec{x}$ = 3j + 5k and $\vec{y}$ = i + 4k.
Solution:

Given: $\vec{x}$ = 3j + 5k and $\vec{y}$ = i + 4k
$\vec{x}$ + $\vec{y}$ = (0 + 1)i + (3 + 0)j + (5 + 4)k