# Plz explain, Is this true about orthogonal vectors?

## Distance between any 2 Orthogonal unit vectors in any inner product space is always equal to $\sqrt{2}$ ?

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:
$c = \sqrt{{a}^{2} + {b}^{2}}$

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

$c = \sqrt{{1}^{2} + {1}^{2}} = \sqrt{2}$

GOOD LUCK