Vector Calculator

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?

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?

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

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.

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  3j  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.