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)

a) Magniyude of u = sqrt[1^2 + 2^2] = sqrt5.
Magnitude of v = sqrt[7^2 + 1^2] = sqrt50.
u . v == (i + 2j) . (7i + j) = 7i . i + i . j + 2j . 7i + 2j . j = 7 + 0 + 0 + 2 = 9.
Therefore, sqrt5 x sqrt50 x cosA = 9, where A is the angle between U and v.
Therefore, A = arccos(9/sqrt5 x sqrt50) = arccos(9/sqrt250) = 55 degree.
Same approach for (b) and (c) that you may try yourself.

我相信 悠閒舒適™ 是誤解了題目
題目中的θ,是指u與v兩個向量之間的夾角
而根據本人了解,閣下找的是UV與x軸之間的角度
並非題目要找的東西

u‧v=│u││v│cosθ

u‧v=1*7+2*1 (個條式a...xa*xa+ya*yb)
│u│=(1^2+2^2)開方=開方5
│v│=(7^2+1^2)開方=5*開方2
咁
9=5*開方10 cosθ
θ=arc cos(9*開方10)/50
其餘個d都係咁,一理通百理明,你得架la

2008-06-13 10:50:00 補充：
基本我答左樓上2號位人兄既野==只係用左中文