How to shift, add, and extended a vector?

Hi All,

I am having trouble figuring out how to shift, add, and extened a vector in MATLAB. I have a picture below to try an illustrate what I am trying to accomplish

I am able to calaculate the angle between the blue vector and green vector. I then want to take the green vector and "shift" it so the tail of the green vector is added to the tip of the lower oragne vector, while maintianing the angle I claculated between the blue and green vector. Finally I want to extend the green vector until it is as long as the second orange vector (meant to illsuarate the final result I am trying to gain), which extends to the dashed blue line that is perpendicular to the second blue vector.

[Jan]

The question is not clear. It confuses me, that there are 2 blue and orange vectors and I do not get, what you want to achieve. In the mathematical definition vectors have now specified position in space, so there is no meaning in "shifting" them. So maybe you are not talking about vectors, but about start points and vectors. Then "adding" or "extending" is trivial: Use + and the multiplication.

You can calculate the angle between two vectors easily:

phi = atan2(norm(cross(a,b)), dot(a,b))

[Zachary Ferrie]

Hi Jan,

I am talking more about start and end points than vectors. That is my mistake. The data I am working with is in an X/Y gird system. The tail of each vector represents a starting X,Y point and the tip of head vector represents a final X,Y point.

I am trying to get to the final X,Y point that would be located at the the tip of the top oragne vector based on the angle between the blue and green vectors.

I hope that helps clarify things a bit. Thank you for the help

[Jan]

Please post, what your inputs are. Then it is much easier to post a solution, because inventing own data migt not match your needs.

"X,Y point that would be located at the the tip of the top oragne vector based on the angle between the blue and green vectors."

This is not clear yet. You have the start point and directions of the orange, blue and green vectors (in which format? [X,Y] coordinate and signed angle between the direction and the X-axis and the length of the vector? Or [X1, Y1; X2, Y2] as start and endpoint of the vectors?). What is now "based on the angle"?

I assume, that actual code has 2 or 3 trivial lines only. But the problem is not explained exactly yet.

[Zachary Ferrie]

Thanks for the input. I think I may have figured out by thinking of my problem more as an intersection of diffrent lines rather than vectors. I will post my results once tested.