Finding coordinates

Hi,

I have problem that needs solving, last time I used maths was ages ago, so this simple exercise is not so simple for me... As you can see in the image below, there three dots on the coordinate axis (x1, x2, x3), the coordinates of which are known; we also know the angles marked alpha1, alpha2 and alpha3. What I need to find is coordinates of Z(a,b), or to prove that they are (0;0) as the dot is on the start of the axis. Hope you can help, any comments appreciated!


http://img51.imageshack.us/img51/702/imag0014o.jpg

Quote:

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Originally Posted by crapmathematician

Hi,

I have problem that needs solving, last time I used maths was ages ago, so this simple exercise is not so simple for me... As you can see in the image below, there three dots on the coordinate axis (x1, x2, x3), the coordinates of which are known; we also know the angles marked alpha1, alpha2 and alpha3. What I need to find is coordinates of Z(a,b), or to prove that they are (0;0) as the dot is on the start of the axis. Hope you can help, any comments appreciated!


http://img51.imageshack.us/img51/702/imag0014o.jpg

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Hi,

you can prove whether or not these lines go through the origin by showing that

, for lines passing through the origin.

Therefore, the line slopes will be

You need to reference all angles to the positive x axis.

Hence

change to

and to