Orthogonal Vector Calculator

This Orthogonal Vector Calculator allows users to input the components of two vectors to compute their dot product, magnitudes, angle between them in both radians and degrees, and determine if the vectors are orthogonal.

Use Our Orthogonal Vector Calculator

Using the Orthogonal Vector Calculator

The Orthogonal Vector Calculator is a tool designed to help you determine the relationship between two vectors in three-dimensional space. This guide will walk you through the process of calculating various properties of the vectors and checking if they are orthogonal.

Step 1: Input the Components of Vector 1

  1. Vector 1 x-component: Enter the x-component of the first vector in the provided field labeled “Vector 1 x-component”. Make sure to use a precise numerical value with a step of 0.01 if necessary.
  2. Vector 1 y-component: Enter the y-component of the first vector in the field labeled “Vector 1 y-component”.
  3. Vector 1 z-component: Complete the input for Vector 1 by entering its z-component in the field labeled “Vector 1 z-component”.

Step 2: Input the Components of Vector 2

  1. Vector 2 x-component: Enter the x-component of the second vector in the field labeled “Vector 2 x-component”.
  2. Vector 2 y-component: Enter the y-component of the second vector in the field labeled “Vector 2 y-component”.
  3. Vector 2 z-component: Enter the z-component of the second vector in the corresponding field labeled “Vector 2 z-component”.

Step 3: Calculate the Results

After entering all components for both vectors, the calculator will automatically compute the following results:

Dot Product: This value is calculated as the sum of the products of corresponding components of the two vectors.

Magnitude of Vector 1: The magnitude reflects the length of the first vector and is calculated using the formula √(x12 + y12 + z12).

Magnitude of Vector 2: Similarly, this value is computed for the second vector using the equivalent formula.

Angle (in radians): The angle between the two vectors is calculated in radians using the cosine inverse function. This requires both dot product and magnitudes of vectors.

Angle (in degrees): To provide the angle in a more standard form, the calculator converts the radian measure into degrees.

Step 4: Determine Orthogonality

Finally, the calculator will indicate whether the vectors are orthogonal based on the dot product. If the absolute value of the dot product is less than 0.0001, the vectors are considered orthogonal, and the result will be “Yes”; otherwise, the result will be “No”.

Review all the calculated results to understand the relationship between the two vectors fully. Whether you’re studying physics, engineering, or mathematics, this tool can greatly assist in analyzing vector properties.