# Plz explain, Is this true about orthogonal vectors?

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Distance between any 2 Orthogonal unit vectors in any inner product space is always equal to #sqrt2# ?

Distance between any 2 Orthogonal unit vectors in any inner product space is always equal to

##### 1 Answer

Jun 15, 2018

Yes.

#### Explanation:

Unit vectors, by definition, have length = 1.

Orthogonal vectors, by definition, are perpendicular to each other, and therefore make a right triangle. The "distance between" the vectors can be taken to mean the hypotenuse of this right triangle, and the length of this is given by the pythagorean theorem:

since, for this case, a and b both = 1, we have

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