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Math Help - "Right-handed" rule with vectors?

  1. #1
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    "Right-handed" rule with vectors?

    Could someone please explain to me how the "right-handed" rule works and how you would use it to appropriate vector questions with it? I understand that you have your right thumb pointing upright and move your thumb the way that the vector moves (or something like that). Although, what I particularly do not understand is how you would be able to answer it with questions. Such as, "True or false: a x (b x a) is perpendicular to a but not to b. (The given diagram that the 'end' of both b and a meet at a high point, whereas the beginning of both b and a come outwards ( /\ <-- basically, with b on the left, a on the right.) I have tried to make sense out of the explanation and examples my textbook has provided although, I am still confused.
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  2. #2
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    To find the direction of \vec{u}\times\vec{v}, hold your right hand so that your index finger is pointing in the direction of \vec{u} and your other fingers curl toward \vec{v}, the your thumb will be pointing in the direction of \vec{u}\times\vec{v}. Basically that just tells you that \vec{u}\times\vec{v} is perpendicular to both \vec{u} and \vec{v} and \vec{u}\times\vec{v}= -\vec{v}\times\vec{u}.

    \vec{b}\times\vec{a} is perpendicular to both \vec{a} and \vec{b} \vec{a}\times (\vec{a}\times\vec{b}) is perpendicular to \vec{a} and \vec{a}\times\vec{b} but not \vec{b}. To see that more clearly, take a specific example: if \vec{b}= \vec{i} and \vec{a}= \vec{j}, then \vec{b}\times\vec{\a}= \vec{i}\times\vec{j}= \vec{k} so that \vec{a}\times(\vec{b}\times\vec{a})= \vec{j}\times\vec{k}= \vec{i}= \vec{b}.
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