Rotating VectorsDate: 12/14/95 at 12:14:7 From: Anonymous Subject: 3D Geometry? Projection? I do not even know how to ask this question because I do not know the names of things or concepts. I don't know where to start... ... but it is this: If I were a vector, say [2,3,4], and I wanted to turn to face another vector, say [-1,10,11], how would I do it? What would I be doing ? I hope you can help me because this REALLY bugs me... Thanks in advance, mlarch@fred.net Date: 7/28/96 at 20:36:6 From: Doctor Jerry Subject: Re: 3D Geometry? Projection? Any two non-zero, non-collinear vectors issuing from the same point form a plane. In this plane, there is an angle t between the two vectors. If we use the standard convention, 0 < t < pi. It may be that you are asking how to rotate one vector so that it falls along the same line as the other. If so, I can tell you how to calculate the angle between the two vectors you gave. Use the law of cosines on the triangle defined by the origin and the ends of the two vectors. The lengths of the vectors are sqrt(29) and sqrt(222). The length of the side opposite the angle t is sqrt(107). So, from the law of cosines, 107 = 222 + 29 - 2*sqrt(222)*sqrt(29)*cos(t). Solving for cos(t), cos(t) = 0.89733... Hence, t = 0.457091... (radians) or 26.189409... (degrees). -Doctor Jerry, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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