Plz explain, Is this true about orthogonal vectors?

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

1 Answer
Jun 15, 2018



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)#