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# C4 vectors

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1. Im finding some vectors quite challenging. Im not sure how i find the point on a vector line which is closest to the origin.

I know what it is perpendular to the orogin. So the vector product equals zero. However i end up forming quadratics which dont lead anywhere.

How should i approach these kinds of questions.

I am given the vector line equation and a point on the line. I am told to find the clostest point to the origin.

Thanks.
2. (Original post by jamesgates1)
Im finding some vectors quite challenging. Im not sure how i find the point on a vector line which is closest to the origin.

I know what it is perpendular to the orogin. So the vector product equals zero. However i end up forming quadratics which dont lead anywhere.

How should i approach these kinds of questions.

I am given the vector line equation and a point on the line. I am told to find the clostest point to the origin.

Thanks.
Well, you know the parametric equation of a point on the plane is (all the english letters are going to be given):

Call this general point

Then you know . Now you need to find s.t where is the direction vector of the line (all this says is make the line OX perpendicuar to your vector line). This gives you a (linear) equation solely in which you can then solve for and then plug this into after which, you then calculate the magnitude of .

I had to make this all very abstract with so many variables because you didn't give me an example to work off, sorry!
3. (Original post by Zacken)
Well, you know the parametric equation of a point on the plane is (all the english letters are going to be given):

Call this general point

Then you know . Now you need to find s.t where is the direction vector of the line (all this says is make the line OX perpendicuar to your vector line). This gives you a (linear) equation solely in which you can then solve for and then plug this into after which, you then calculate the magnitude of .

I had to make this all very abstract with so many variables because you didn't give me an example to work off, sorry!
Thanks. I understand it now!
4. (Original post by jamesgates1)
Thanks. I understand it now!
No problem, make sure to test it out on a few problems but it's usually a method that has served me very well.

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