中四數學題

1. vector a is ( i - 2 j) and let vector b be ( mi+ nj)

| a | = sq root ( 1 + 4)
= sq root 5

a。b= | a | | b | cos angle
= sq root 5 x 3 sq root 3 x cos 180
=-3 sq root 15

a。b = ( i - 2 j) 。 ( mi+ nj)
= m - 2n

1 st equation ..... m- 2n = - 3 sq root 15

let Q vector a = - vector b
Qi - 2Qj = -mi -nj
Q = - m and - 2 Q = -n

2nd equation .... -2m = n
sloving the 2 equations
m = -3/5 sq root 15 and n = 6/5 sq root 15

therefore the coordinate of b is (-3/5 sq root 15 , 6/5 sq root 15)

--------------------------------------------------------------------------------------

2. a。b = 1 x 1 x cos 60
= 1/2

後面唔係好明條題目問乜....

1. 向量b 與向量a (1,-2)的夾角為180度,且絕對值向量b = 3√3,求坐標b

解:
設b=k(1,-2)
=> ｜b｜=｜k｜√5
但｜b｜=3√3
k=正負(3√15)/5
b=[正負(3√15)/5](1,-2)
=( (3√15)/5 , (-6√15)/5 ) 或 ( (-3√15)/5 , (6√15)/5 )