Exercise 1.105: Show that: (a) x (UA) = (U) x A + U (xA) (b) . (AxB) = B. (xA) - A. (xB).

Exercise 1.112: if A x B = 8 i - 14 j + k and A + B = 5 i + 3 j + 2 k, find A and B

Exercise 1.113: Let l1, m1, n1 and l2, m2, n2 be the directing cosines of two vectors. Show that the angle between them is such that cos = l1l2 + m1m2 + n1n2

Exercise 1,114: Show that the line joining the midpoints of two sides of a triangle is parallel to the third side and is half its length.

Exercise 1,120: Show that A. dA / dt = AdA / dt