There are four operations in vectors -

**Vector addition,****Vector Subtraction,****Vector Dot product and****Vector cross product.**

Here in this page only Vector addition and subtraction formula have being discussed and the remaining formulas are discussed in other pages. Vector addition triangular law and parallelogram law given as below.

Triangular law of addition : If two forces

Parallelogram law of addition : If two forces

Vector Subtraction : If two forces

Vector Formulas are useful in simple calculations of vectors. It helps to find the resultant vector if the two vectors are given.

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Calculate Vector | Adding Vectors Calculator |

Angle between Two Vectors Calculator | eigen vector calculator |

Below are problems based on vector addition and subtraction which may be helpful for you.

### Solved Examples

**Question 1: **If two forces represented by $\vec{A}$ = 5 $\vec{i}$ + 2 $\vec{j}$ - 3 $\vec{k}$ and $\vec{B}$ = 3 $\vec{i}$ - 2 $\vec{j}$ + 4 $\vec{k}$ are acting in the same direction, calculate the resultant force.

** Solution: **

Let $\vec{A}$ = 5 $\vec{i}$ + 2 $\vec{j}$ - 3 $\vec{k}$,

$\vec{B}$ = 3 $\vec{i}$ - 2 $\vec{j}$ + 4 $\vec{k}$

$\vec{A}$ + $\vec{B}$ = 5 $\vec{i}$ + 2 $\vec{j}$ - 3 $\vec{k}$ + $\vec{B}$ + 3 $\vec{i}$ - 2 $\vec{j}$ + 4 $\vec{k}$

= 8 $\vec{i}$ + $\vec{k}$.

The Resultant force R = 8 $\vec{i}$ + $\vec{k}$.

**Question 2: **If two forces $\vec{A}$ = 2 $\vec{i}$ - 3 $\vec{k}$ and $\vec{B}$ = - 2 $\vec{i}$ + 7 $\vec{j}$ + 4 $\vec{k}$ are acting in the direction opposite to each other. Calculate the Resultant force.

** Solution: **

Let $\vec{A}$ = 2 $\vec{i}$ - 3 $\vec{k}$,

$\vec{B}$ = - 2 $\vec{i}$ + 7 $\vec{j}$ + 4 $\vec{k}$

$\vec{A}$ - $\vec{B}$ = 2 $\vec{i}$ - 3 $\vec{k}$ - (- 2 $\vec{i}$ + 7 $\vec{j}$ + 4 $\vec{k}$).

= 4 $\vec{i}$ - 7 $\vec{j}$ - 7 $\vec{k}$

The Resultant force R = 4 $\vec{i}$ - 7 $\vec{j}$ - 7 $\vec{k}$.

Let $\vec{A}$ = 5 $\vec{i}$ + 2 $\vec{j}$ - 3 $\vec{k}$,

$\vec{B}$ = 3 $\vec{i}$ - 2 $\vec{j}$ + 4 $\vec{k}$

$\vec{A}$ + $\vec{B}$ = 5 $\vec{i}$ + 2 $\vec{j}$ - 3 $\vec{k}$ + $\vec{B}$ + 3 $\vec{i}$ - 2 $\vec{j}$ + 4 $\vec{k}$

= 8 $\vec{i}$ + $\vec{k}$.

The Resultant force R = 8 $\vec{i}$ + $\vec{k}$.

Let $\vec{A}$ = 2 $\vec{i}$ - 3 $\vec{k}$,

$\vec{B}$ = - 2 $\vec{i}$ + 7 $\vec{j}$ + 4 $\vec{k}$

$\vec{A}$ - $\vec{B}$ = 2 $\vec{i}$ - 3 $\vec{k}$ - (- 2 $\vec{i}$ + 7 $\vec{j}$ + 4 $\vec{k}$).

= 4 $\vec{i}$ - 7 $\vec{j}$ - 7 $\vec{k}$

The Resultant force R = 4 $\vec{i}$ - 7 $\vec{j}$ - 7 $\vec{k}$.

More topics in Vector Formulas | |

Unit Vector Formula | Dot Product Formula |

Cross Product Formula | Vector Projection Formula |