Cross product order of operations

[John777]

Could someone please clarify a simple order of operations related to cross product?


A x (B x C) = ?


I am not sure between the these two options:

= (A X B) x (A X C)

or

= do stuff in parenthesis first then cross with A

 

[chiro]

Could someone please clarify a simple order of operations related to cross product?


A x (B x C) = ?


I am not sure between the these two options:

= (A X B) x (A X C)

or

= do stuff in parenthesis first then cross with A

You use the same rules of algebra that you use in vector algebra. Brackets first, then your cross products then your +/-.

For example 1 you calculate B x C then A x Result, for second you calculate A x C, then A x B, and then result 2 x result 1. As you are probably aware cross product is not commutative so order is important.

Hope that helps.

 

[HallsofIvy]

Could someone please clarify a simple order of operations related to cross product?


A x (B x C) = ?


I am not sure between the these two options:

= (A X B) x (A X C)

A x (B x C) is definitely NOT equal to (A x B) x (B x C) for exactly the reason that 5(3x 2) is NOT equal to (5x3)x(5x2)! Why would you think it would be?

For one thing, if A is parallel to either B or C, one of A x B or A x C would be 0. But B x C would be perpendicular to both B and C and so perpendicular to A so that would NOT be true.

or

= do stuff in parenthesis first then cross with A

You are really asking "should I do something totally random or do what the formula tells me to do?" If you want to get the right answer, my suggestion is that you do what the formula tells you to do!