Author Topic: Techniques and methods for vectors (Read 637 times) Tweet Share

VCE_2012 · « **on:** January 02, 2012, 04:25:12 pm »

Hello again, can someone list 'some' vector techniques or methods that are not shown in VCE text books, that is quicker and more convenient.
One example maybe: If the point K divides the line PQ internally in the ratio l:m and the position vectors of P,Q and K with respect to O are 'p' and 'q' and 'k' then: k=(mp+lq)/(l+m)

hargao · « **Reply #1 on:** January 02, 2012, 11:33:04 pm »

If you want to find the shortest distance between a vector line and a given point, three methods can be used.

Let the line L be defined by the vector equation $L:\textbf{r}=\textbf{a}+t\textbf{b}, where~t\in R$
Let the given point be called $P$
Let $d$ be the shortest distance between the given point and the vector line.
(use the attached diagram to make life easier)

Method 1:
Find $N$ using the relationship:
$\vec{PN}\cdot\textbf{b}=0$

The distance $d=|\vec{PN}|$

Method 2:
Select a convenient point A on the line L, and find the angle $\theta$ between $\vec{AP}$ and $\textbf{b}$ using the relationship:
$\vec{AP}\cdot \textbf{b}=|\vec{AP}||\textbf{b}|cos(\theta)$

The distance $d=|\vec{AP}|sin(\theta)$

Method 3:
The distance $d=|\vec{AP}|sin(\theta)=\frac{|\vec{AP}\times \textbf{b}|}{|\textbf{b}|}$

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Author Topic: Techniques and methods for vectors (Read 637 times) Tweet Share

VCE_2012

Techniques and methods for vectors

hargao

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