The angle and distance between the two vectors.
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In a two-dimensional vector space, assume that there is one vector u(a, b) and another unknown vector v(c, d). If I knew angle and distance between these two vectors, how can I calculate the unknown vector v? I means the elements of a vector v. If I can calculate, how should I apply in Matalb??
Thank you very much.
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YongHyun
2017년 2월 14일
Both vectors have origin (0,0) and the distance means the distance between the end points of the vector. Thanks.
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Roger Stafford
2017년 2월 14일
You have a known vector u = [a,b] and an unknown vector v = [c,d]. The distance as you have defined it is a known
r = sqrt((c-a)^2+(d-b)^2)
and the angle in radians measured counterclockwise from u to v is a known A. You are to find v.
B = atan2(b,a);
C = cos(A+B);
S = sin(A+B);
t1 = a*C+b*S+sqrt(r^2-(a*S-b*C)^2);
t2 = a*C+b*S-sqrt(r^2-(a*S-b*C)^2);
c1 = t1*C;
d1 = t1*S;
c2 = t2*C;
d2 = t2*S;
v1 = [c1,d1];
v2 = [c2,d2];
As you can see, there will generally be two real solutions or none.
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Roger Stafford
2017년 2월 14일
편집: Roger Stafford
2017년 2월 14일
Yes, you're right Jan. If the line of the vector happens to be exactly tangent to the circle of radius r, there will be just one solution. That's why I qualified my statement with the word 'generally'.
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