# Vector Calculator

Fill the table and press the make graph button to use vector calculator

Magnitude
Angle (Â°)
x
y

Dot Product
ab
0
bc
0
cd
0
=
0
0
0
0

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

1. On entering magnitude and angle, it gives x and y components of the vector.
2. When you enter a second vector, it performs vector addition on the two vectors at the bottom.
3. 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?

“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?

The 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

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:

6i  7j   1k and 3i  2j  0k

Solution:

6i  7j  1k

+ 3i  2j  0k

____________

9i  9j  1k

## 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 = 9i  3 2k and B = 1i  1j  1k

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.