(C4) I've been stuck on this vector question for an hour? :(

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rambo1168
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http://www.examsolutions.net/a-level...June/paper.php

It's question 5b)

I just don't get it
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WishingChaff
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What specifically don't you get?

Can you post your attempt at the solution?
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Kim-Jong-Illest
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(Original post by rambo1168)
http://www.examsolutions.net/a-level...June/paper.php

It's question 5b)

I just don't get it
how do ya prove 2 vectors are perpendicular? If P lies on l, is there any way you can find co-ordinates for it (in terms of lambda)? You can figure out what OP is from this. You also are given the direction of l.
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TMaths6
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Factorise it;
r= (6+l)i + (19+4l)j + (-1-1l)k

If two vectors are perpendicular, their dot product is 0.
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rambo1168
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(Original post by WishingChaff)
What specifically don't you get?

Can you post your attempt at the solution?
I know that if there's two lines that are perpendicular, a.b=0 .. But I don't know what to put a or b as


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Asadprince
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It's the dot product rule. If two lines are perpendicular then you know the a.b = 0 because cos90=0.

And you know both direction vectors... Go forth and multiply


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Asadprince
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Is is the direction vector for l1, and you can work out the direction vector of OP which is straight forward as it's simply the the Equation of L1


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WishingChaff
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Ok. Well you are told that the vector OP is perpendicular to the line l. You know the direction vector of the line l. What is that?

Now you want to find the vector OP. Well we are told it is on the line l, thus we can just say the vector OP is:

(x,y,z) = (6,19,-1) + lambda (1,4,-2) for some lambda. Your objective now is to find lambda?

So you now have equations for x,y and z, write them out. Also, you have the condition that (x,y,z) and (1,4,-2) are perpendicular. Thus solve the simultaneous equations for lambda. What do you get?

(Original post by rambo1168)
I know that if there's two lines that are perpendicular, a.b=0 .. But I don't know what to put a or b as


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Asadprince
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Hope that explains things better


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TMaths6
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(Original post by rambo1168)
I know that if there's two lines that are perpendicular, a.b=0 .. But I don't know what to put a or b as


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a is the direction vector of the line L1 (i +4j -2k) and b is the direction vector of the OP

P must be on the line L1. So P must have coordinates (6+l)i + (19+4l)j + (-1-2l)k, for some particular value of l (which you are trying to find out)

O (The origin) has coordinates 0i +0j + 0k

So the direction vector of OP is
(6+l)i + (19+4l)j + (-1-2l)k - 0i +0j + 0k

=(6+l)i + (19+4l)j + (-1-2l)k

Now you have a and b
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Phichi
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(Original post by Asadprince)
Name:  ImageUploadedByStudent Room1397148025.483748.jpg
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Hope that explains things better


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The whole idea here is to help the person, not answer the question for them.
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