VERY quick cross product question

[bcjochim07]

Homework Statement

p X q - r

Homework Equations

The Attempt at a Solution

In order to evaluate this expression, I must first evaluate q - r and then perform the cross product, right? I'm trying to think about X as an operator, like del, that operates on the things that appear after it. Is this correct?

Thanks.

 

[Mark44]

I would think it's the other way around: that you do the cross product first, and then subtract. The only justification I can think of for doing it this way comes from arithmetic--that multiplication and division are to be done before addition and subtraction.

For example, the expression 2*4 - 3 = 8 - 3 = 5. I don't recall seeing this idea extended to vector cross products, though.

The symbol X used in cross products affects the two things on either side of it, not just what follows it, so for that reason it is different from the del operator or the differentiation operator.

 

[HallsofIvy]

Yes, I agree with Mark44. By the standard "precedence" of operations, $p \times q- r$ means $(p\times q)- r$, not $p\times (q- r)$

 

[tiny-tim]

Same with del … ∇A - B ≠ ∇(A - B)