Find u v lull llvll and du v for the given inner product def

Find (u, v), lull, llvll, and d(u, v) for the given inner product defined on R u (1, 1, 1), v (2, 5, 2), (u, v) u1v1 3u 2v2 u3v3 (a) (u, v) (b) lull (c) (d) u, v)

Solution

(a)

Given that, u= (1,1,1) and v=(2,5,2)

So, u1=1,u2=1,u3=1 & v1=2,v2=5,v3=2

Also, it is given that (u,v) = u1v1+3u2v2+u3v3

So, (u,v)= (2,15,2).

(b)

Also, ||u||= |u|= sqrt(1^2 + 1^2 +1^2)= 1.732

(c)

Similarly, ||v||= |v|= sqrt(33) = 5.74

(d)

d(u,v) = ?(