maths~~~~~

http://img51.imageshack.us/i/86137587.png/

a) a . b = abs(a) abs(b) cos x = 2 x 3 x cos 120 = - 3.
b) By drawing : a + b is the diagonal of the parallelogram with sides a and b. Length of diagonal = abs ( a + b).
By calculation: (a + b). ( a + b) = a . a + 2 a. b + b . b = [abs(a)]^2 + 2 a . b + [abs(b)]^2 = 2^2 + 2(-3) + 3^2 = 4 - 6 + 9 = 7 = [abs(a + b)]^2. So abs(a + b) = sqrt 7.
c)
(a + b) . (2a + kb) = 2a.a + (2 +k)(a . b) + kb.b = (2)(2^2) + (2 +k)(-3) + k(3^2)
= 8 - 6 - 3k + 9k = 2 + 6k = 0 , since the 2 vectors are perpendicular to each other. So k = -1/3.
cii)
(3a + 2b) . (3a + 2b) = 9a.a + 12 a. b + 4 b. b = 9(2^2) + 12(-3) + 4(3^2)
= 36 - 36 + 36 = 36 = [abs(3a + 2b)]^2. So abs(3a + 2b) = sqrt 36 = 6.
That is the magnitude of -hc = 6. Since c is a unit vector, so -h = 6, h = -6.

|a| , |b| 之間的角 = ???