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# Vectors - Equation of a line Watch

1. Equation of a line. I have no idea what most of this means.Can someone please explain this to me?

http://imgur.com/HOO95iw
2. Bump. Anyone? :/
3. (Original post by theonn)
Equation of a line. I have no idea what most of this means.Can someone please explain this to me?

http://imgur.com/HOO95iw
Are you studying this for A level?

It's just giving you the standard parameterised form of a line in terms of vectors;

if A is a known point on the line, then you can express the position vector of a general point P on the line as:

position vector of A + some scalar multiple of the direction vector of the line
4. (Original post by theonn)
Bump. Anyone? :/
So point A has coordiantes (2,3). The gradient of it is 1/2, which you can clearly see from the diagram. So if we want to write in vector form how to get from the origin to point A, we denote this OA.

OA=2i+3j. This means that to get from the origin to point A, we go along 2 in the x-direction and up 3 in the y direction.

Similarly to get to OP, we to first go to point A, and then we have to go some scalar multiple in the direction of vector m, and since we don't know what this is we call it lamda.

5. (Original post by davros)
Are you studying this for A level?

It's just giving you the standard parameterised form of a line in terms of vectors;

if A is a known point on the line, then you can express the position vector of a general point P on the line as:

position vector of A + some scalar multiple of the direction vector of the line
Studying comp sci, we have maths modules which are essentially A-Level/some bits of GCSE work into it. I understand that OA = a =2i+3j. But I don't understand what the gradient m is, how how I it comes up, or where that red line comes from. Also the r the lamda sign. Can you explain this to me in basic simple terms please? If you can. I'd really appropriate it
6. (Original post by Music99)
So point A has coordiantes (2,3). The gradient of it is 1/2, which you can clearly see from the diagram. So if we want to write in vector form how to get from the origin to point A, we denote this OA.

OA=2i+3j. This means that to get from the origin to point A, we go along 2 in the x-direction and up 3 in the y direction.

Similarly to get to OP, we to first go to point A, and then we have to go some scalar multiple in the direction of vector m, and since we don't know what this is we call it lamda.

I understand how to get to point A, and that to get to point P we must start off from point A. But I don't understand how we got the figure for Gradient m = 2i + j. I'm still really confused
7. (Original post by theonn)
Studying comp sci, we have maths modules which are essentially A-Level/some bits of GCSE work into it. I understand that OA = a =2i+3j. But I don't understand what the gradient m is, how how I it comes up, or where that red line comes from. Also the r the lamda sign. Can you explain this to me in basic simple terms please? If you can. I'd really appropriate it
The red line is just showing steps along and up, it's not really part of the maths!

The principle is that the line you want has a particular direction (what they call the gradient) which is 2i+j, However, there are lots of lines parallel to that line which will have the same gradient! The line we're interested in must contain A as a point, and to get to a general point on the line we go from O to A and then along the line its direction by a particular fraction. Lambda gives you the multiple of the direction you go along - it's just an ordinary number like 2, 7, 0.5 etc

So one point on the line has position OA + 2(2i + j), another has position vector OA + 17(2i+j) etc
8. (Original post by theonn)
I understand how to get to point A, and that to get to point P we must start off from point A. But I don't understand how we got the figure for Gradient m = 2i + j. I'm still really confused
gradient is change in y over change in x.

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