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10.
(a) Find two vectors in with Euclidean norm 1 whose Euclidean inner product with (3, −1) is zero.
(b) Show that there are infinitely many vectors in with Euclidean norm 1 whose Euclidean inner product with (1, −3,
5) is zero.
Find the Euclidean distance between u and v.
11.
(a) ,
(b) ,
(c) ,
(d) ,
Verify parts (b), (e), (f), and (g) of Theorem 4.1.1 for ,, , , and
12. .
Verify parts (b) and (c) of Theorem 4.1.2 for the values of u, v, w, and k in Exercise 12.
13.
In each part, determine whether the given vectors are orthogonal.
14.
(a) ,
(b) ,
(c) ,
(d) ,
(e) ,
(f) ,
For which values of k are u and v orthogonal?
15.
