Vector Question ~~ help

2007-02-22 10:05 pm
Vector a = 2i - j , b = 3i - αj , find α 的值使 a and b 之間的夾角是 π/3

回答 (1)

2007-02-22 11:00 pm
✔ 最佳答案
assume α > 0,

tan d = sin d / cos d

with a = 2i - j
tan m = -1/2

with b = 3i - αj
tan n = -α/3

n - m = π/3
so, -1/2 + tan (π/3) = -α/3

α = -3 (-1/2 + sqrt(3)) = 3/2 + 3*sqrt(3)

2007-02-22 15:07:27 補充:
Sorry, it should be...n - m = -π/3so, n = m - π/3tan n = tan m - tan π/3tan n = tan m - sqrt(3)-α/3 = -1/2 - sqrt(3)α = 3/2 + 3*sqrt(3)


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