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(b) How would you define the Euclidean length of the “diagonal” of the box in part (a)?
Figure Ex-33
34.
(a) Suppose that u and v are vectors in . Show that
(b) The result in part (a) states a theorem about parallelograms in . What is the theorem?
35. and , then
(a) If u and v are orthogonal vectors in such that
_________ .
(b) Draw a picture to illustrate this result.
In the accompanying figure the vectors u, v, and form a triangle in , and denotes the
36. angle between u and v. It follows from the law of cosines in trigonometry that
Do you think that this formula still holds if u and v are vectors in ? Justify your answer.
Figure Ex-36
Indicate whether each statement is always true or sometimes false. Justify your answer by giving
37. a logical argument or a counterexample.
