Worksheet to find Angle between two Vectors

The vector angle is used to describe the angle difference of physical quantities which have a magnitude and a direction associated with them. The vector angle is calculated from the endpoint of the first line to the endpoint of the second line. The endpoint is determined by the vector direction in which the line was measured. This worksheet help you to understand how to calculate vector angle.

Example:
Let A and B are two vectors and C is the resultant vector.
A = 1i+2j+3k
B = 4i+5j+6k

Step 1
Find the scalar or dot product of two vectors:
The result of dot product is represented by X,
X = 32

Step 2
Calculate the magnitude of two vectors and represented as M1 and M2,
M1 = 3.742
M2 = 8.775

Step 3
Find the angle between two vectors,
C = cos^-1(X/M1.M2)* (180/π)
(or)
We can use the general formula
C = cos^-1(A.B/|A|.|B|)*(180/π)

When you try such calculations on your own, this angle between vectors calculator can be used to verify the results of your calculations.