Determine if three vectors form a right hand triple?

[fredrick08]

Homework Statement

ok can someone tell me how to determine if three vectors form a right hand triple? and why does (a-b)x(a+b)=2(axb)...

please someone help, I am really confused on how to do these... arent just three vectors a right hand triple if the dot product between them all is 0?? I am not sure though please someone help.. and the second one.. the must be a formula or a property i can't find... thanks

 

[HallsofIvy]

Homework Statement

ok can someone tell me how to determine if three vectors form a right hand triple? and why does (a-b)x(a+b)=2(axb)...

please someone help, I am really confused on how to do these... arent just three vectors a right hand triple if the dot product between them all is 0?? I am not sure though please someone help.. and the second one.. the must be a formula or a property i can't find... thanks

Well, first of all what is the definition of "right hand triple"? That would seem a good place to start!

For the second, I assume that you are talking about the cross product of vectors. (a- b)x(a+ b)= what if you just go ahead and multiply it out (the distributive and associative laws of multiplication are true for the cross product). Now remember that cross product if anti-commutative. What is axa? What is bxb?