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Calc3.2.CrossProductProof (view source)
Revision as of 05:34, February 28, 2010
, 05:34, February 28, 2010→Third Identity
If either <math>\vec{q}_*, \vec{r}_*=\vec{0}</math>, then the identity we seek is certainly true, and if they are collinear, then one is a multiple of the other and the identity we seek follows from application of our first two identities.
If either <math>\vec{q}_*, \vec{r}_*=\vec{0}</math>, then the identity we seek is certainly true, and if they are collinear, then one is a multiple of the other and the identity we seek follows from application of our first two identities.
[[Image:Cross product plane.jpg|right|200px|thumb|We imagine <math>\vec{p}</math> sticking out of the screen towards the reader. You may need to enlarge this picture.]]
So, let us assume that <math>\vec{q}_*, \vec{r}_*</math> both have non-zero magnitude and are not collinear. If we imagine <math>\vec{p}</math> sticking out of our computer monitors, pointing towards the reader, then the vectors in questions all look something like the picture on the right.
So, let us assume that <math>\vec{q}_*, \vec{r}_*</math> both have non-zero magnitude and are not collinear. If we imagine <math>\vec{p}</math> sticking out of our computer monitors, pointing towards the reader, then the vectors in questions all look something like the picture on the right.
==Notes==
==Notes==
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