Is (a × b) × c zero when c is perpendicular to both a and b?

[Chen]

It's given that vector c is perpendicular to both vectors a and b. Which of the following is true:

1) http://phstudy.technion.ac.il/~wn114071/physweb/question/1_4_01.gif
(a x b) x c
2) http://phstudy.technion.ac.il/~wn114071/physweb/question/1_4_02.gif
(a x c) dot b
3) http://phstudy.technion.ac.il/~wn114071/physweb/question/1_4_03.gif
(a x c) x b
4) http://phstudy.technion.ac.il/~wn114071/physweb/question/1_4_04.gif
(a x b) dot c

Can someone please just confirm the answer is (1) because I have only one attempt left at submitting an answer for this question.

Thanks

 

[Galileo]

I can't open the files. You need authorization for that...

 

[Chen]

I knew that might happen, so I wrote the expression in each link below. (1) is (a x b) x c, i.e (a cross b) cross c.

Thanks.

 

[quantumdude]

It's impossible to say which one is true, because those are all expressions, not equations.

 

[BobG]

Answers 2 and 4 give you a scalar number. The absolute value is the same for both, but the sign changes.

Answer 1 gives you a null vector (all components equal to 0) since the cross product of A and B is either in the same direction as C or the exact opposite direction of C.

Answer 3 gives you a vector.