Constant vector and cross product?

[jlmac2001]

Okay, here's the question:

For r=xi + yj +zk evaluate grad x (k x r), where k is a constant vector.

I know how to do the cross product of k x r and I know how to do
grad x (k x r). But I don't know what k is. What's k?

 

[Doc Al]

Originally posted by jlmac2001
... But I don't know what k is. What's k?

Try assuming an arbitrary k vector: ai + bj + ck (or whatever). Then see what happens.

 

[jlmac2001]

does this look right?

The answer I got is: -2ai-2bj-2ck

 

[Doc Al]

Originally posted by jlmac2001
The answer I got is: -2ai-2bj-2ck

I got 2k (where k is the constant vector) but I did it quick. (So my answer differs by a minus sign from yours.) My main point was that you didn't have to know the value of k (the a, b, & c) to do the problem.

 

[jlmac2001]

question

how did you just get 2k? i don't understand

 

[Doc Al]

Originally posted by jlmac2001
how did you just get 2k? i don't understand

By "2k" I mean: 2ai + 2bj + 2ck. (The same as you, but with a + instead of -.) 2\vec{k} is what I should have written. Make sense?

 

[jlmac2001]

thanks

i get it now