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C4 Need help with a vectors question and quick revision for Integration. watch

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    I would appreciate it if anyone out there can solve this vectors question for me, which is below. I would also like if anyone can quickly explain integration to me because my maths teacher didn't explain it to our class. (I know it sucks, but it isn't his fault for having cancer, I hope he gets better soon). Anyway the sub teacher seems like he doesn't what he's explaining, or we just didn't understand him. Here's the vectors question (I solved all of it except for part d] ).

    Page 84, Mixed Excercise 5K Q. 11 (Official Edexcel textbook)

    Referred to a fixed origin O, the points A and B have position vectors (5i-j-k) and (i-5j+7k) respectively.

    a) Find an equation of the line AB.

    b) Show that the point C with position vector 4i-2j+k lies on AB.

    c) Show that OC is perpendicular to AB.

    d) Find the position vector of the point D, where D is not equal to A, on AB such that |OD| = |OA|

    Any help is much appreciated. Thanks.
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    a) Equation AB = A + \lambda(B-A)

    b) Make three equations, one of each dimension:
    A + \lambda(B-A) = C
    and show that \lambda is constant for each equation.

    c)cos\theta = \frac{a.b}{|a||b|} = \frac{AB.OC}{|AB|\times|OC|}

    Therefore, if AB.OC = 0 they are perpendicular.
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    Basic integration is easily explained.

    Differentation you decreased the power by one and multiplied by the old power.
    With Integration you increase the power by one and divide by the new power.

    e.g. Integrate 4x = 2x^2.
    Integrate 5x^2 = 5/3 x^3.

    Same applies whens theres brackets

    Integrate (5x+9)^2 = 1/15 (5x+9)^3 (differentiate inside the bracket and divide by that as well as dividing by the new power.)
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    Thanks guys, but maxfire you answered all the questions except for d), which is the only one i needed, and DDave thanks for explaining to me basic integration, I already know that from C1, but i need help with much more complicated integration like integration by parts and separation of variables. I'm sorry if i wasted your time, but if you can still help me, then thanks again.
 
 
 
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Updated: January 22, 2010
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