# Addition and subtraction of vectors

**Addition of vectors**(

**sum of vectors**)

c_{i} = a_{i} + b_{i}

**Subtraction of vectors**(

**difference of vectors**)

c_{i} = a_{i} - b_{i}

## Addition and subtraction of vectors - formulas

### The formulas of addition and subtraction of vectors for plane problems

In the case of the plane problem the sum and difference of vectors a = {a_{x} ; a_{y}} and b = {b_{x} ; b_{y}} can be found using the following formulas:

a + b = {a_{x} + b_{x}; a_{y} + b_{y}}

a - b = {a_{x} - b_{x}; a_{y} - b_{y}}

### The formulas of addition and subtraction of vectors for spatial problems

In the case of the spatial problem the sum and difference of vectors a = {a_{x} ; a_{y} ; a_{z}} and b = {b_{x} ; b_{y} ; b_{z}} can be found using the following formulas:

a + b = {a_{x} + b_{x}; a_{y} + b_{y}; a_{z} + b_{z}}

a - b = {a_{x} - b_{x}; a_{y} - b_{y}; a_{z} - b_{z}}

### The formulas of addition and subtraction of vectors for n dimensional space problems

In the case of the n dimensional space problem the sum and difference of vectors a = {a_{1} ; a_{2} ; ... ; a_{n}} and b = {b_{1} ; b_{2} ; ... ; b_{n}} can be found using the following formulas:

a + b = {a_{1} + b_{1}; a_{2} + b_{2}; ... ; a_{n} + b_{n}}

a - b = {a_{1} - b_{1}; a_{2} - b_{2}; ... ; a_{n} - b_{n}}

## Addition and subtraction of vectors - examples

### Examples of plane tasks

**Solution:**

**Solution:**

### Examples of spatial tasks

**Solution:**

**Solution:**

### Examples of n dimensional space tasks

**Solution:**

**Solution:**

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