I really need some help about vector product. (Specially cross multiplication) And i want an answer with explanation of the value of \[\vec{a}\times \vec{b}= ?\] where \[\vec{a}= \frac{2\vec{x}+\vec{y}}{3}\]
And \[\vec{b}= \frac{2\vec{p}+\vec{q}}{3}\]
Need help for vector product
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You spin my head right round right round,
When you go down, when you go down down......(-$from$ "$THE$ $UGLY$ $TRUTH$" )
When you go down, when you go down down......(-$from$ "$THE$ $UGLY$ $TRUTH$" )
Re: Need help for vector product
Physically the cross product means the area of a parallelogram with two adjacent sides $\vec{a},\vec{b}$.
$\dfrac{2\vec{x}+\vec{y}}{3}$ means the position vector of a point which has $\vec{x}$ and $\vec{y}$ as the position vector of the terminal points (and the segment between those two terminal points is divided into ratio $2:1$ by the first point).
I don't think that we can specifically conclude anything special from just these equations. We need more info about what we want to prove.
$\dfrac{2\vec{x}+\vec{y}}{3}$ means the position vector of a point which has $\vec{x}$ and $\vec{y}$ as the position vector of the terminal points (and the segment between those two terminal points is divided into ratio $2:1$ by the first point).
I don't think that we can specifically conclude anything special from just these equations. We need more info about what we want to prove.
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin
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Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.
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Re: Need help for vector product
In 3 d space to calculate the vector product you must know about three axis .Here you dont mentioned about axis and its not possible to give answer according to given condition
Re: Need help for vector product
from the information you have given, the only thing that can be found is:
$\vec{a}\times \vec{b}= \frac{4}{9} \vec{x} \times \vec{p} + \frac{2}{9} \vec{x} \times \vec{q} + \frac{2}{9} \vec{y} \times \vec{p} + \frac{1}{9} \vec{y} \times \vec{q}$
$\vec{a}\times \vec{b}= \frac{4}{9} \vec{x} \times \vec{p} + \frac{2}{9} \vec{x} \times \vec{q} + \frac{2}{9} \vec{y} \times \vec{p} + \frac{1}{9} \vec{y} \times \vec{q}$
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Re: Need help for vector product
Oh! I forget to mention, it is 2d space. (Actually i got it when i was solving a Geometry Unbound problem)
You spin my head right round right round,
When you go down, when you go down down......(-$from$ "$THE$ $UGLY$ $TRUTH$" )
When you go down, when you go down down......(-$from$ "$THE$ $UGLY$ $TRUTH$" )