Does scalar multiplication affect the cross product of vectors?

[amy098yay]

Mod note: Member warned about posting with no effort.

1. Homework Statement
Expand to the general case to explore how the cross product behaves under scalar multiplication k (a x b) = (ka) x b = a x (kb).

The Attempt at a Solution

would this be the right general case to portray the situation?

 

[jedishrfu]

Can't you use the definition of vector cross product?

ie A x B = | A | * | B | * sin ( angleAB ) u

Where u is the unit vector perpendicular to both A and B such that A, B, and u form a right handed system.

EDIT amended the definition where I left out the unit vector part.

 

[Mark44]

You need to show an attempt. Normally I would issue a warning and possibly infraction points. You were hit with several points a day or so ago, and your posts have improved considerably, so I'll treat this one more informally.

The problem as you state it seems to be to prove that k (a x b) = (ka) x b = a x (kb). What you posted in the Word document is not any kind of attempt -- it seems to be just the statement of some larger problem

Please put your work directly in the input pane here - not in a PDF or Word file or other attachment. It's frustrating to have to open another window to view the work. Having the work right here makes it easier for us to insert a comment right where there is a problem.

One other thing. All of these vector problems fall under precalculus, not calculus, so I am moving this thread to that section (and leaving a forward link).

 

[amy098yay]

alright thanks

 

[LCKurtz]

Can't you use the definition of vector cross product?

ie A x B = | A | * | B | * sin ( angleAB )

That isn't the definition of the cross product. It is also incorrect. It is $|A\times B|$ that equals the right side but it still isn't the definition because $A\times B$ is a vector, not a scalar.

 

[Mark44]

alright thanks

To do this (i.e., prove that k (a x b) = (ka) x b = a x (kb) ), let a, b, and c be arbitrary vectors such as a = <a₁, a₂, a₃>, b = <b₁, b₂, b₃>, and similar for c, and let k be an arbitrary scalar. Do not use specific numbers. Calculate all three cross products and show that they are all equal.

 

[jedishrfu]

Sorry folks I left the unit vector part out in my haste to answer the question.