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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: Nato on November 25, 2012, 02:45:01 pm

Title: annoying vectors question!!
Post by: Nato on November 25, 2012, 02:45:01 pm: hey everyone

i have a attached a vectors question which i am reeeaaallly stuck on, any help would be greatly appreciated.
in particular, i need help which question "b" and "c"

thank you
Title: Re: annoying vectors question!!
Post by: polar on November 25, 2012, 03:01:25 pm: (b)
$\begin{aligned}\vec{AP} &= 2\vec{PB} \\ \text{so, \;} \vec{AB} &= 3\vec{PB} \\ \vec{PB} &= \frac{1}{3}\vec{AB} \\ &= \frac{1}{3}(\bold{b}-\bold{a})\end{aligned}$

(c)
$\begin{aligned} \vec{AP} &= 2\vec{PB} \\ \vec{OP} - \vec{OA} &= 2(\vec{OB} - \vec{OP}) \\ \vec{OP} + 2\vec{OP} &= \vec{OA} + 2\vec{OB} \\ 3\vec{OP} &= \vec{OA} + 2\vec{OB} \\ \vec{OP} &= \frac{1}{3}(\bold{a} + 2\bold{b}) \end{aligned}$
Title: Re: annoying vectors question!!
Post by: Nato on November 25, 2012, 03:08:16 pm: thanks i understand (b), but could you please clarify your working for (c)?
Title: Re: annoying vectors question!!
Post by: polar on November 25, 2012, 03:16:23 pm: the question stated that $\vec{AP} = 2\vec{PB}$ , the vector joining point A to point P can be found by evaluating $\vec{OP} - \vec{OA}$ , similarly, $\vec{PB} = \vec{OB} - \vec{OP}$ , using these you can go backwards to find everything in terms of OA, OB and OP to solve for OP
Title: Re: annoying vectors question!!
Post by: Nato on November 25, 2012, 03:32:26 pm: crystal clear now, thanks man