Question

How do you know if two vectors are orthonormal?

Answer 1

Hint: In this question, we need to tell when two vectors are orthonormal. First, we will understand the concept of orthonormal. The meaning of orthonormal is perpendicular or we can say that orthogonal.

Complete step by step solution:
Let us discuss the key concepts such as orthonormal vectors. We can say that an orthonormal set is formed by a collection of vectors that are all mutually perpendicular (right angles) and of unit length (they have a length of one). That means, in simple words, the two vectors are orthonormal if and only if they are perpendicular to each other and also both the vectors are of unit length.

Therefore, if two vectors are orthonormal then they are perpendicular and are of unit length.

Additional Information:Here, we can say that the word orthonormal is a combination of two words such as ortho and normal. The word “ortho” means perpendicular and the word “normal” means two vectors have a unit length. For two vectors to be orthonormal, these vectors should be linearly independent. Also, the group of vectors is said to be linearly independent if and only if any one of them can be expressed as a linear combination of the others.

Note:Many students generally get confused with the terms orthonormal and orthogonal. The difference between them is in the case of orthonormal vectors, both the vectors are of unit length. This makes a big difference between orthogonal and orthonormal vectors.