(Vector) How to express a vector in terms of another vector? (1 Viewer)

catha230 · Dec 23, 2019

Screen Shot 2019-12-23 at 6.49.58 am.png

For question 15c), I am not quite sure what to do to express those vectors in terms of the other vectors. I have never come across any similar questions nor have I ever learnt any formula applicable to this. Could someome please explain to me the concept behind it and give me a hint to solve this question? Thank you so much in advance.

Drdusk · Dec 23, 2019

catha230 said:
View attachment 27932

For question 15c), I am not quite sure what to do to express those vectors in terms of the other vectors. I have never come across any similar questions nor have I ever learnt any formula applicable to this. Could someome please explain to me the concept behind it and give me a hint to solve this question? Thank you so much in advance.

I'll do just one of them so you get an idea.
You need to recall the property that for any vector say XY

$\overrightarrow{\text{XY}} = \overrightarrow{\text{Y}} -\overrightarrow{\text{X}} \Rightarrow \overrightarrow{\text{BD}} = \overrightarrow{\text{D}} - \overrightarrow{\text{B}}$

$= \overrightarrow{\text{OD}} - \overrightarrow{\text{OB}} = \overrightarrow{r} - \overrightarrow{p}$

Drongoski · Dec 23, 2019

c)

$\overrightarrow {BD} = \overrightarrow {OD} - \overrightarrow {OB} = \vec r - \vec p \\ \\ \overrightarrow {BC} = \overrightarrow {OC} - \overrightarrow {OB} = \vec q - \vec p\\ \\ \overrightarrow {DC} = \overright {OC} - \overrightarrow {OD} = \vec q - \vec r$

d)
$\overrightarrow {BC} \bullet \overrightarrow {BC} $ and $ \overrightarrow {DC} \bullet \overrightarrow {DC}$
represent, resp. the square of BC and the square of DC, which are equal.

$\therefore (\vec q - \vec p)\bullet (\vec q - \vec p) = (\vec q - \vec r)\bullet (\vec q - \vec r)$

(Vector) How to express a vector in terms of another vector? (1 Viewer)

catha230

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Drongoski

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