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# C4 - Vectors

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1. Find a unit vector ai + bj + ck which is perpendicular to the two vectors 2i + 2j -k and 4i + 2k

I understand for two vectors to be perpendicular their dot product must be 0, provided they are both non zero vectors.

So I worked out the dot product for the vector I am trying to find, and the two vectors given.

2a + 2b - c = 0 and 4a + 2c = 0

Is this right so far? I don't think there is a way to solve them like this
2. Find the cross product of the two vectors, then divide each coefficient of i, j and k by a constant, such that it's magnitude is 1. If you don't know how to do this yet then I'll explain a little more, but you won't learn anything if I just give you the answer haha.
3. for this you need to remember there wont be a unique solution as if (x,y,z) is perp then so will k(x,y,z)

so if you could write

a=kb
b=b
c=lb

for some k,l then your vector would be b(k,1,l) and then choose b so its a unit vector.
4. (Original post by James94)
Find the cross product of the two vectors, then divide each coefficient of i, j and k by a constant, such that it's magnitude is 1. If you don't know how to do this yet then I'll explain a little more, but you won't learn anything if I just give you the answer haha.
So you find the point of intersection of the two vectors given, is that what you mean by cross product? I know what a unit vector is, its a vector of magnitude 1. So you divide each component of the vector by the magnitude of the initial vector.
5. Cross product is meant to help you arrive at a vector which is perpendicular to the original constituents.

ie a cross b produces a vector n; this vector n is perpendicular to both a and b.

Cross product is not solving for intersections whatsoever.

Hope this helps. Peace.
6. Just thought I'd add that the cross product is not required for Edexcel C4.

Also, remember that it isn't the exact values of what you've called a, b and c you are actually interested in - it's their relative values. You can make up any number and use it for a, b or c (it's usually easiest to use 1) and then solve your two simultaneous equations to find the other two.
7. What would be the best way for revising for vectors. I find them the hardest in C4
Thanks
8. (Original post by bkhan)
What would be the best way for revising for vectors. I find them the hardest in C4
Thanks
Do lots and lots and lots of questions - they don't deviate too much from the norm.
9. You can't find a specific solution as there are more variables than equations,but you can write each in terms of the others: e.g.

a + b + c = 0
2a + c = 0

so c = -2a, and b = a, so you have a vector (a, a, -2a), and then just let a be a constant such that the vector (a, a, -2a) has length is 1

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