Show that the set of vectors in Rn is orthogonal.

Question

Consider the following.

{(−1, 5), (15, 3)}

(a) Show that the set of vectors in Rⁿ is orthogonal.

(−1, 5) · (15, 3) = 

(b) Normalize the set to produce an orthonormal set.

Answer 1

Two vectors are orthogonal (perpendicular) if the dot product is equal to zero, "0".

To normalize a vector divide each coordinate by the magnitude of the vector.