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How to find if a vector is parallel to another

by dark_omen
Tags: parallel, vector
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dark_omen
#1
Sep19-06, 05:31 PM
P: 9
Okay, so I have two vectors a = <-6, 9, -3> and b = <2, -3, 1>. How can I test to see if these two vectors are parallel or not?
Thanks
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radou
#2
Sep19-06, 05:41 PM
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Vectors a and b are parallel if there exists a real number c such that a=cb. In your case it is pretty obvious.
dark_omen
#3
Sep19-06, 05:49 PM
P: 9
What if it is not so obvious like the one I presented. Is there another approach to it (cross product of dot product ??)
Thanks

radou
#4
Sep19-06, 06:07 PM
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How to find if a vector is parallel to another

Think about the definition of the cross product, and see what happens. Btw, just use axb=[tex]det \left(\begin{array}{ccc}\vec{i} & \vec{j} & \vec{k}\\a_{1} & a_{2} & a_{3}\\b_{1} & b_{2} & b_{3}\end{array}\right)[/tex] for a=cb.


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