The vector calculator performs several calculations on up to 10 vectors. The list of its functions is as follows:

- On entering magnitude and angle, it gives x and y components of the vector.
- When you enter a second vector, it performs vector addition on the two vectors at the bottom.
- On the right side, it also gives the dot product between two vectors.

## How to use the Vector Calculator?

To find the angle and magnitude of a vector using this calculator, follow these steps.

**To find the vector components: **Enter the magnitude and the angle.

**To find the vector sum and dot product:** Enter the magnitude and angle of second vectors.

## What is a vector?

A vector is defined as:

“An object that has a magnitude and a direction.”

A vector has two points. First is the starting point which is called the tail and the ending point is called the head.

## How to find the components of a vector?

Components of a vector are calculated using magnitude and angle. The formulas used are;

X-Component = |F|cos????

Y-Component = |F|sin????

**Example:**

Find the components of force whose magnitude is 20N and is acting at an angle of 45 degrees.

**Solution:**

**Step 1:** Identify the values.

Magnitude = 20 N

Angle = 35 degrees

**Step 2:** Put in the formulas.

X-Component = |F|cos????

X-Component = |20|cos35

X-Component = **16.3830**

Y-Component = |F|sin????

Y-Component = |20|sin45

Y-Component = **14.14**

## How to add vectors?

The same units are added together. You have to add the magnitude of the *i * unit vector of the first vector into the *i * unit vector of the second vector and so on.

**Example:**

Add the following vectors.

6*i *7**j** 1**k** and * *3*i *2**j** 0*k*

**Solution:**

6*i *7**j** 1**k**

+ 3*i *2**j** 0*k*

** ____________**

9*i *9**j** 1*k*

## How to multiply two vectors using a dot product?

The dot product is written in mathematical form as

**A**.**B** = |A||B|cos????

**Example:**

Multiply the vectors **A** and **B**.

A = 9*i *3**j ** 2**k** and B = 1*i *1**j** 1**k**

The angle between the vectors is 20 degrees.

**Solution:**

Find the magnitudes of **A** and **B**.

|A| = √ ((9)^{2}+(3)^{2}+(2)^{2})

|A| = (81+9+4)^{½}

|A| = **9.69**

|B| = √ ((1)^{2}+(1)^{2}+(1)^{2})

|B| = (1+1+1)^{½}

|B| = **1.73**

Now use it in the formula.

**A**.**B** = |9.69||1.73|cos 20

**A.B = 15.752**

**Note: **Enter the angle between two vectors as the angle of the first vector. The calculator will automatically assume the other vector along the x-axis.