Show that if v is a nonzero vector in R^n, then (1/||v||)v has Euclidean norm 1?

Answer 1

||(1/||v||)v|| = (1/||v||)||v|| = 1. This is because ||av|| = |a| ||v|| for any scalar a.

Answer 2

(a million/||v||)v ||v|| is merely the dimensions of v, so in case you divide a vector by potential of its length, you will get a unit vector. occasion: v = 4i +3j II v II = sqrt (sixteen + 9) = 5 The vector v has length 5 and makes an perspective of 50 3° with the x-axis, in case you divide this vector by potential of 5, you will get a unit vector with same direction and sense.