Inner Product Calculator

The Inner Product Calculator allows users to compute the inner product, magnitudes of two vectors, and the angle between them for either 2D or 3D vectors with precision.

Use Our Inner Product Calculator

How to Use the Inner Product Calculator

This guide provides step-by-step instructions on how to use the Inner Product Calculator. This tool enables you to calculate the inner product, magnitudes, and angle between two vectors in either 2D or 3D space.

Step 1: Selecting the Vector Dimension

  • Select the vector dimension: Choose between 2D Vector or 3D Vector by selecting the appropriate option from the dropdown menu labeled “Vector Dimension”. This selection determines whether you will be working with two-dimensional or three-dimensional vectors.

Step 2: Inputting Vector Components

For 2D Vectors:

  • Enter the x-component of the first vector in the field labeled “Vector 1 – x component”.
  • Enter the y-component of the first vector in the field labeled “Vector 1 – y component”.
  • Enter the x-component of the second vector in the field labeled “Vector 2 – x component”.
  • Enter the y-component of the second vector in the field labeled “Vector 2 – y component”.

For 3D Vectors:

  • In addition to the x and y components, enter the z-component of the first vector in the field labeled “Vector 1 – z component”.
  • Enter the z-component of the second vector in the field labeled “Vector 2 – z component”.

The values for x, y, and z components should be numbers, and all fields are required. The calculator accepts real numbers, so use integers or decimals as needed.

Step 3: Calculating the Results

  • Once you have entered all the necessary components for the vectors, the calculator will automatically compute the following results:
    • Inner Product: The calculator finds the inner product (dot product) of the two vectors. For 2D vectors, it calculates x1 * x2 + y1 * y2. For 3D vectors, it computes x1 * x2 + y1 * y2 + z1 * z2.
    • Magnitude of Vector 1: This is calculated using the formula sqrt(x1² + y1²) for 2D and sqrt(x1² + y1² + z1²) for 3D vectors.
    • Magnitude of Vector 2: Similarly, this uses sqrt(x2² + y2²) for 2D and sqrt(x2² + y2² + z2²) for 3D vectors.
    • Angle Between Vectors (degrees): This uses the formula acos(innerProduct / (magnitude1 * magnitude2)) * 180 / π to find the angle between the two vectors in degrees.

The results are displayed with precision, rounded to four decimal places for the magnitudes and inner product, and two decimal places for the angle.