Enter the vector coordinate values of the velocity and acceleration into the calculator to determine the angle between them.

Angle Between Vectors Formula

The following formula is used to calculate the angle between two vectors. 

A= acos[(a (dot) b) / (||A||*||B||)]
  • Where A is the angle between the vectors
  • a (dot) b is the dot product between the two vectors
  • ||A|| is the magnitude of vector A
  • ||B|| is the magnitude of vector B

To calculate the angle between the acceleration and velocity vectors, calculate the dot product of the two vectors, then divide by the product of the magnitudes of each vector.

What are velocity and acceleration vectors?

Definition:

Velocity and acceleration vectors are 3-Dimensional representations of the physical properties of velocity and acceleration.

How to calculate the angle between velocity and acceleration vectors?

Example Problem:

The following example outlines how to calculate the angle between a velocity and acceleration vector.

First, determine the velocity vector. For this example, the velocity vector is (1,2,3).

Next, determine the magnitude of the velocity vector. This is equal to 3.741.

Next, determine the acceleration vector. For this problem, the acceleration is (4,5,6).

Next, calculate the magnitude of the vector. This is 8.7749.

Finally, calculate the angle between the vectors using the formula above:

A= acos[(a (dot) b) / (||A||*||B||)]

A= acos[(32) / 32.87]

A = 13.211 degrees