The angle between twovctors 2i+2j and (m-4)i+(m+4)j is
where sin =4/5,Find the possible value(s) of m
amaths
2008-01-13 7:42 pm
回答 (2)
2008-01-13 9:08 pm
✔ 最佳答案
sin =4/5 then cos = 3/5 or -3/5cos of the angle = {(2i+2j)．[(m-4)i+(m+4)j]} / [ |2i+2j| |(m-4)i+(m+4)j| ]
square the both sides
9 / 25 = 16m^2 / [ (8) (2m^2 + 32) ]
m^2 = 9
m = 3 or -3
2008-01-13 9:43 pm
cos²θ = 1 - sin²θ
cos²θ = 1 - 16/25
cos²θ = 9/25
cosθ = ± 3/5
when cosθ = 3/5
3/5 = [ 2 * (m–4) + 2 * (m+4)] / [ √( 2²+2²) * √[(m+4)²+(m-4)²]
3/5 = 4m/4√(m²+16)
√(m²+16) = 5m/3
m² + 16 = 25m²/9
16m²/9 = 16
m = ± 3
when cosθ = - 3/5
- 3/5 = [ 2 * (m–4) + 2 * (m+4)] / [ √( 2²+2²) * √[(m+4)²+(m-4)²]
- 3/5 = 4m/4√(m²+16)
√(m²+16) = - 5m/3
m² - 16 = 25m²/9
16m²/9 = 16
m = ± 3
so, m = ± 3
cos²θ = 1 - 16/25
cos²θ = 9/25
cosθ = ± 3/5
when cosθ = 3/5
3/5 = [ 2 * (m–4) + 2 * (m+4)] / [ √( 2²+2²) * √[(m+4)²+(m-4)²]
3/5 = 4m/4√(m²+16)
√(m²+16) = 5m/3
m² + 16 = 25m²/9
16m²/9 = 16
m = ± 3
when cosθ = - 3/5
- 3/5 = [ 2 * (m–4) + 2 * (m+4)] / [ √( 2²+2²) * √[(m+4)²+(m-4)²]
- 3/5 = 4m/4√(m²+16)
√(m²+16) = - 5m/3
m² - 16 = 25m²/9
16m²/9 = 16
m = ± 3
so, m = ± 3
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https://hk.answers.yahoo.com/question/index?qid=20080113000051KK01177