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les Institution H2 Mathematics 2019 Year 5 The points Á, B, C and D have position vectors a, b, c and d with respect to the origin O. %3D Show that m, the position vector of M on AC such that AAM = µMC, where 1+H=1 is given by m = Aa+ µc. Deduce further that |m = 2|a| +Hc-A4la - cf. %3D +la². Show that if ABCD is a rectangle, then a + c = b* +d. (i) (i) Show that if A, B, C and D are points on a sphere, centered at 0, and if AC where A'BM = µ'MD , with l+u'=1 , then %3D meets BD at M , Aµ|a-cf = 2'µ'|b-df . %3D

les Institution H2 Mathematics 2019 Year 5 The points Á, B, C and D have position vectors a, b, c and d with respect to the origin O. %3D Show that m, the position vector of M on AC such that AAM = µMC, where 1+H=1 is given by m = Aa+ µc. Deduce further that |m = 2|a| +Hc-A4la - cf. %3D +la². Show that if ABCD is a rectangle, then a + c = b* +d. (i) (i) Show that if A, B, C and D are points on a sphere, centered at 0, and if AC where A'BM = µ'MD , with l+u'=1 , then %3D meets BD at M , Aµ|a-cf = 2'µ'|b-df . %3D

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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les Institution H2 Mathematics 2019 Year 5 The points Á, B, C and D have position vectors a, b, c and d with respect to the origin O. %3D Show that m, the position vector of M on AC such that AAM = µMC, where 1+H=1 is given by m = Aa+ µc. Deduce further that |m = 2|a| +Hc-A4la - cf. %3D +la². Show that if ABCD is a rectangle, then a + c = b* +d. (i) (i) Show that if A, B, C and D are points on a sphere, centered at 0, and if AC where A'BM = µ'MD , with l+u'=1 , then %3D meets BD at M , Aµ|a-cf = 2'µ'|b-df . %3D
Transcribed Image Text:les Institution H2 Mathematics 2019 Year 5 The points Á, B, C and D have position vectors a, b, c and d with respect to the origin O. %3D Show that m, the position vector of M on AC such that AAM = µMC, where 1+H=1 is given by m = Aa+ µc. Deduce further that |m = 2|a| +Hc-A4la - cf. %3D +la². Show that if ABCD is a rectangle, then a + c = b* +d. (i) (i) Show that if A, B, C and D are points on a sphere, centered at 0, and if AC where A'BM = µ'MD , with l+u'=1 , then %3D meets BD at M , Aµ|a-cf = 2'µ'|b-df . %3D
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