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junior college 2 | H2 Maths
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help me for vectors
Date Posted: 8 months ago
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QR = λPQ
r = q + λ(q - p) = (1 + λ) q - λp
m = 1/2 r = (1 + λ)/2 q - λ/2 p
f = βq
FP = μPM
p - f = μm - μp
(2 + 2μ + λμ)p - (μ + λμ + 2β)q = 0
Since p and q are non-parallel and non-zero implies the coefficients of p and q are 0
2 + 2μ + λμ = 0
μ + λμ + 2β = 0
Making β the subject in terms of μ
β = (1 + λ)/(2 + λ)
f : q - f = β : 1 - β = 1 + λ : 1
r = q + λ(q - p) = (1 + λ) q - λp
m = 1/2 r = (1 + λ)/2 q - λ/2 p
f = βq
FP = μPM
p - f = μm - μp
(2 + 2μ + λμ)p - (μ + λμ + 2β)q = 0
Since p and q are non-parallel and non-zero implies the coefficients of p and q are 0
2 + 2μ + λμ = 0
μ + λμ + 2β = 0
Making β the subject in terms of μ
β = (1 + λ)/(2 + λ)
f : q - f = β : 1 - β = 1 + λ : 1
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