Ｆ．５Ａ．ＭＡＴＨＳＸ１

Let A= 3i + 4j
B = (c + 1)i + (c - 1)j
Magnitude of A = sqrt(3^2 + 4^2) = 5.
Magnitude of B = sqrt[(c + 1)^2 + (c - 1)^2] = sqrt(2c^2 + 2)
A dot B = (3i + 4j) dot [(c + 1)i + (c - 1)j] = 3c + 3 + 4c - 4 = 7c - 1
so 7c - 1 = 5 sqrt(2c^2 + 2) cos x
7c - 1= 5 sqrt(2c^2 + 2)(1/5sqrt 2)
7c - 1 = sqrt(2c^2 + 2)/sqrt 2
7c - 1 = sqrt(c^2 + 1)
49c^2 + 1 - 14c = c^2 + 1
48c^2 - 14c = 0
2c(24c - 7) = 0
so c = 0 or 7/24.
For x to be smaller than 90 degree, c = 7/24.







2009-09-20 19:41:13 補充：
c = 0 is for cos x = -1/5sqrt 2.