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Need help, URGENT maths question: (2 Viewers)

1008

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I believe this Q. was asked here before, and answered by Sy123: http://community.boredofstudies.org...1437/intermediate-value-theorem-question.html .
Thanks for that InteGrand.

I have another question. What would be the quickest method to do this?



The method I know involves converting the plane to a Cartesian equation and then substituting the x1, x2 and x3 variables of the cartesian equation with the line. This took very long for this question, and I got it wrong...
 

InteGrand

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Thanks for that InteGrand.

I have another question. What would be the quickest method to do this?



The method I know involves converting the plane to a Cartesian equation and then substituting the x1, x2 and x3 variables of the cartesian equation with the line. This took very long for this question, and I got it wrong...
The method you used isn't too long, and will lead to the right answer if done correctly. You'll basically end up with the plane equation of the form ax + by + cz = d . Then sub. in the line coordinates to this and solve for lambda (which is easy to solve for since it's just a linear equation in lambda), and then sub. this solution back into the parametric equation for the line.

Another way to do it is to equate the RHS's of both plane and line equations and try solve for lambda (and mu and xi, though you'll only need lambda, but you might want to get mu and xi too for checking purposes). This will involve using Gaussian Elimination.
 

1008

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The method you used isn't too long, and will lead to the right answer if done correctly. You'll basically end up with the plane equation of the form ax + by + cz = d . Then sub. in the line coordinates to this and solve for lambda (which is easy to solve for since it's just a linear equation in lambda), and then sub. this solution back into the parametric equation for the line.

Another way to do it is to equate the RHS's of both plane and line equations and try solve for lambda (and mu and xi, though you'll only need lambda, but you might want to get mu and xi too for checking purposes). This will involve using Gaussian Elimination.
Thanks for the reply InteGrand. I was thinking, isn't there a method to do this using dot products and/or cross product? The answer to this question was the point (3,2,2), which just happens to be the point in the line equation...
 

InteGrand

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Thanks for the reply InteGrand. I was thinking, isn't there a method to do this using dot products and/or cross product? The answer to this question was the point (3,2,2), which just happens to be the point in the line equation...
Well it's basically a coincidence it happened to the point they give in the line's parametric equation (because they could have used a whole host of other points for the exact same line's equation (i.e. any other point on that line)).

The cross product would be used to find a normal to the plane, which would then allow us to find the Cartesian equation of the plane.
 

1008

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Well it's basically a coincidence it happened to the point they give in the line's parametric equation (because they could have used a whole host of other points for the exact same line's equation (i.e. any other point on that line)).

The cross product would be used to find a normal to the plane, which would then allow us to find the Cartesian equation of the plane.
Could you please demonstrate how one would go about doing this?
 

1008

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I dunno how to do C though...
 
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InteGrand

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I dunno how to do C though...
To do part b), the change of variable should be l = k-1, rather than +1 (it's (the change of variables and limits of summation) done basically like how we'd do a change of variables in integration).
 

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Replies are not generated within a matter of 10 seconds of algorithms. They're generated out of niceness in helping others
I know I know. Guys a beast. Wanna know what he studies/does for a living
 

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