Question

show uxv is orthogonal to u and v.
u=2i-j+2k
v=3i-j-3k

Answer 1

Would I be able to just say here: If u and v are nonzero vectors, than by the geometric properties of cross products uxv is orthogonal to both u and v?

Answer 2

I don't understand how I can prove those to be nonzero vectors though, or if it would be necessary to do so

Answer 3

Using cross products, uxv gives a vector. If you can obtain that vector, I recommend that you do, otherwise drop me a line. That vector should have a cross-product of zero with both u and v. You can test this by taking the cross-products.

Here's a link to the MIT Linear Algebra course if you're going to have more questions on this subject: http://openstudy.com/study?version=feed:join-study-group&referrer=mit%2018.06%20linear%20algebra,%20spring%202010&domain=ocw.mit.edu#/groups/MIT%2018.06%20Linear%20Algebra%2C%20Spring%202010

Answer 4

uxv gave me a matrix. Can I get a single vector from it?

Answer 5

Or...is the cross product the determinant of that matrix given?

Answer 6

What is their dot product?

Answer 7

I think this is a physics problem. Physics has specific rules for how cross-products work with vectors written in orthogonal coordinates. Basically, if your write \[\left[\begin{matrix}i & j & k & i & j\\ i & j & k & i & j\\ i & j & k & i & j\end{matrix}\right]\], the cross product is positive if you can draw a diagonal down and to the right and negative if you have to go down and left (from the first row to the second in axb, the answer will be c if you went down and right, -c if you wend down and left, and 0 if you went straight down). The cross-product is also equal to the determinant you mentioned (because of the properties of 3X3 determinants)

Answer 8

@eolis223 find the cross product then dot it with one of them :)

Answer 9

I got 5i+23j+k for uxv. Correct?

Answer 10

j isn't right

Answer 11

Test it by dot products with the original vectors. 23 seems more than a little high.

Answer 12

excuse me, 12j not 23

Answer 13

yep

Answer 14

I got it guys, thanks

Answer 15

Which means it's bed time. Let this be a lesson to you people (especially Fibonacci, who dealt with me for the last hour). You should not drink and derive. Rum and theoretical math do not mix well. goodnight

Answer 16

np lol and actually I got slammed the night before my final for theory and it helped alot maybe that is your problem, you're not drunk enough lol

Answer 17

That's possible. Though I haven't been drunk at any point this evening, just merry

Answer 18

Good night though, and thanks for the help

Answer 19

np and night