How To Find The Angle Between Two Vectors

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How to Find the Angle Between Two Vectors: Video Lesson

Angle Between Two Vectors Calculator

The calculator below calculates the angle between 2D and 3D vectors. Simply enter the components of each vector in the form the 3 by 1 column matrix x y z

How to Find the Angle Between Two Vectors

To find the angle between two vectors:

  1. Find the dot product of the two vectors.
  2. Divide this by the magnitude of the first vector.
  3. Divide this by the magnitude of the second vector.
  4. Take the inverse cosine of this value to obtain the angle.

For example, find the angle between the 2 by 1 column matrix 3 negative 2 and the 2 by 1 column matrix 1 7.

Step 1. Find the dot product of the two vectors

To find the dot product of two vectors, multiply the corresponding components together and add them up.

The dot product of two 2D vectors the 2 by 1 column matrix Row 1: a. sub x Row 2: a. sub y andthe 2 by 1 column matrix Row 1: b sub x Row 2: b sub y is found using a. times b equals a. sub x b sub x plus a. sub y b sub y.

For vectors the 2 by 1 column matrix 3 negative 2 and the 2 by 1 column matrix 1 7, the dot product a. times b equals open paren 3 times 1 close paren plus open paren negative 2 times 7 close paren.

Therefore a. times b equals 3 minus 14

a. times b equals negative 11

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