The angle and distance between the two vectors.
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Yonghyun
le 13 Fév 2017
Modifié(e) : Roger Stafford
le 14 Fév 2017
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.
2 commentaires
YongHyun
le 14 Fév 2017
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
le 14 Fév 2017
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.
2 commentaires
Roger Stafford
le 14 Fév 2017
Modifié(e) : Roger Stafford
le 14 Fév 2017
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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