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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: squance on February 06, 2009, 11:01:45 pm

Title: Vectors! Eek! need help please
Post by: squance on February 06, 2009, 11:01:45 pm: Need help with a question from essential spesh maths .
Ex 2B question 6.

A and B are points defined respectively by position vectors a = i + j -5k and b = 3i -2j-k. M is a point on AB such that AM: MB=4:1.

Find:
i) the OM vector
ii). Find the coordinates of M
Title: Re: Vectors! Eek! need help please
Post by: Flaming_Arrow on February 06, 2009, 11:18:37 pm: a.

$\frac{\vec{AM}}{\vec{MB}} = \frac{4}{1}$

$\vec{AM} = 4\vec{MB}$

$AB = AM + MB$

$AB = 5MB$

$AB =5(MO + OB)$

$2i-3j+4k = 5(MO+ 3i -2j-k)$

$2i-3j+4k = 5MO + 15i-10j-5k$

$\frac{-13i+7j+9k}{5}=MO$

$\therefore \vec{OM} = \frac{13i-7j-9k}{5}$

b.

coordinates are $(\frac{13}{5},\frac{-7}{5},\frac{-9}{5})$
Title: Re: Vectors! Eek! need help please
Post by: squance on February 06, 2009, 11:25:43 pm: Thanks for the thorough response :D
My sis muchly appreciates it!