A.Maths - 兩向量的純量積 附加數高手請進(急急急急急急急急急急急急急急急)

1.(a) a.b
=丨a丨丨b丨cos120ﾟ
=3*4*-0.5
=-6
(b) (a + b) . (a - b)
= 丨a丨²- 丨b丨² + a . b - a . b
= 9 - 16
= -7
(c) 丨a + b丨²
= (a + b) . (a + b)
= 丨a丨² + 丨b丨² + 2a . b
= 9 + 16 -12
=13
(d) ( a - 2b) . (3a + b)
= 3丨a丨² - 2丨b丨² - 6a . b + a . b
= 27 - 32 + 30
= 25

2. (a) (3i - 2j) . (-i + 2j)
= 3*(-1) - 2*2
= -7
(b) (-5i + 3j) . (2i - 4j)
= (-5)*2 - 3*4
= -22