Author Topic: Vectors help please (Read 1141 times) Tweet Share

Nato · « **on:** November 23, 2012, 08:38:35 pm »

Hi all,

i have attached the problem I am having difficulty solving/understading.

could someone please solve and explain question b to me.

thank you

polar · « **Reply #1 on:** November 24, 2012, 11:05:32 am »

(a) it's easier if you find a path from A to B, in this case it is A to D, D to C, C to B
$\begin{aligned} \vec{AB} &= \vec{AD} + \vec{DC} + \vec{CB} \\ &= \vec{AD} + \vec{DC} - \vec{BC} \\ &= \bold{q} + k\bold{p} - \bold{r} \\ \bold{p} - k\bold{p} &= \bold{q} - \bold{r} \\ \bold{p} &= \frac{1}{1-k}(\bold{q} - \bold{r}) \end{aligned}$

(b) find a path from F to E - F to A, A to B, B to E
$\begin{aligned} \vec{FE} &= \vec{FA} + \vec{AB} + \vec{BE} \\ &= -\vec{AF} + \vec{AB} + \vec{BE} \\ &= -2\bold{q} + \bold{p} + 2\bold{r} \\ &= -2(\bold{q} - \bold{r}) + \bold{p} \\ \text{Let \;} \bold{s} &= \bold{q} - \bold{r} \\ \vec{FE} &= -2\bold{s} +\bold{p}\end{aligned}$
however, the question asks for FE in terms of k and $\bold{p}$ only, you have to use the information in part (a)
since $\bold{q} - \bold{r} = (1-k)\bold{p}$ , $\bold{s} = (1-k)\bold{p}$

substituting $\bold{s}$ into $\vec{FE}$ gives
$\begin{aligned} \vec{FE} &= -2(1-k)\bold{p} + \bold{p} \\ &= 2k\bold{p} - \bold{p} \\ &= (2k-1)\bold{p} \end{aligned}$

hence, $\vec{FE}$ is parallel to $\vec{DC}$ since there exists a $\lambda$ such that $\vec{FE} = \lambda\vec{DC}$ where $\vec{FE} = \frac{2k-1}{k}\vec{DC}$

(c) equate coefficients in this part
$\begin{aligned}\vec{FE} &= 4\vec{AB} \\ (2k-1)\bold{p} &= 4\bold{p} \\ 2k-1 &= 4 \\ k &= \frac{5}{2}\end{aligned}$

Nato · « **Reply #2 on:** November 25, 2012, 02:56:08 pm »

thank you so much Polar, you have helped me understand the question.

Search the forums now!

We have moved!

Author Topic: Vectors help please (Read 1141 times) Tweet Share

Nato

Vectors help please

polar

Re: Vectors help please

Nato

Re: Vectors help please

Recent Posts

User:
Password: