a-maths~~~~~

(a) a。b = |a| |b| cos120˚= 2 x 3 x (-0.5) = -3

(b) |a + b|^2 = |a|^2 + |b|^2 - 2|a| |b| cos ( 180˚ - 120˚ )
= 4 + 9 - 12 cos 60˚
= 13 - 6
= 7

(c) (i) ( a + b )。( 2a + kb ) = 0
2|a|^2 + ka。b + 2a。b + k|b|^2 = 0
8 - 3k - 6 + 9k = 0
2 + 6k = 0
k = -1 / 3

(ii) 3a + 2b + hc = 0
hc = -3a - 2b
h|c| = |-3a - 2b|
c is a unit vector, |c| = 1
h = |-3a - 2b|
|-3a - 2b|^2 = |3a|^2 + |2b|^2 - 2 |3a| |2b| cos ( 180˚ - 120˚ )
= 36 + 36 - 2 x 6 x 6 cos 60˚
= 72 - 72 x 0.5
=36
h^2 = 36
h = 6

Alternative method:
|-3a| = 6
|-2b| = 6
Angle between -3a and -2b is 60˚
|-3a|, |-2b| and |-3a - 2b| are three sides of an equilateral triangle.
|-3a - 2b| = 6
h = 6

這裏可以幫到你
http://yayantw.test.hansawell.net/yahoo.com.hk/hk/auction/1118037410