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sleepysmurf
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#1
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#1
How do you find the vector equation of a line when you have the vector equation of two planes which meet in the line?
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bloodhound
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#2
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instead of r in r.n=a for both planes put (x,y,z) and u will get two simultaneous equation. but u cant generally solved two sim equations for 3 variables so you have to get all the solutions in term of another variable. i choose to write x and y in terms of z and then put z=lamda. and then carry on from there. i cant remember from there i will have to look it up again.
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Rich
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Originally posted by sleepysmurf
How do you find the vector equation of a line when you have the vector equation of two planes which meet in the line?
From the vector equation of the planes, rewrite them in the form r.n = a.n and then from there it is easy to write them in Cartesian form. You now have two equations in three unknowns (x, y and z), which will generally give you a line of solutions. To find this line, choose one of the unknowns (e.g. x) and write the other two variables in terms of this chosen one only. Set the chosen one equal to a parameter and then you have the other two variables in terms of this parameter only, so you have the equation of the line in parametric form, and you can then easily move from parametric form to vector form.

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sleepysmurf
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Thanks a lot.
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cayley-hamilton
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workout the cross/vector product of the Normal of the two planes (which is simply the coefficients of the cartesian equations). This gives the direction vector of a line perpendicular to both normals -ie the common line (and to find the equation subs a know value to find constant vector)
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bloodhound
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Originally posted by rahaydenuk
From the vector equation of the planes, rewrite them in the form r.n = a.n and then from there it is easy to write them in Cartesian form. You now have two equations in three unknowns (x, y and z), which will generally give you a line of solutions. To find this line, choose one of the unknowns (e.g. x) and write the other two variables in terms of this chosen one only. Set the chosen one equal to a parameter and then you have the other two variables in terms of this parameter only, so you have the equation of the line in parametric form, and you can then easily move from parametric form to vector form.

Regards,

thats bloody what i said!!!!!!!!!!! its plagarism!!!!!!!!
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Rich
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#7
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Originally posted by bloodhound
thats bloody what i said!!!!!!!!!!! its plagarism!!!!!!!!
No it's not, you hadn't posted when I clicked 'Reply'!
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bloodhound
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#8
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as you can clearly see, my post is before yours. so i posted mine before
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Rich
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#9
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Originally posted by bloodhound
as you can clearly see, my post is before yours. so i posted mine before
I don't contend that you posted your reply before I posted mine, what I was saying is that when I clicked the 'Reply' button on the main thread page to go to the reply screen, you had not posted your message. You must therefore have posted your message whilst I was typing out my reply, therefore I didn't know that you'd already posted a response when I sent mine.

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bloodhound
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#10
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oh sorry. its alrite then. we both know about maths and thats alrite!! hurray. Peace is so much better than war
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bloodhound
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#11
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#11
ours answers are virtually identical anyway
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Rich
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#12
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Originally posted by bloodhound
oh sorry. its alrite then. we both know about maths and thats alrite!! hurray. Peace is so much better than war
Don't worry, I didn't mean to sound aggressive.

No we don't want any wars!
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