# cross

1. ### Cross Product

- the problem The matrix problem below: Below is an example problem:
2. ### cross product - 3

= a X b ?? b X a ? b X a = ??

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5. ### cross product and torque

There is an example in my online calculus course showing how to find the torque produces when a force is applied at an angle to a horizontal wrench with a length of 30cm. There is a sentence that says, The wrench is 40cm long, so |vec r| = 0.4. They don't have an explanation as to how they...
6. ### Help with cross product vector question

I have a cross product question asking the following, Given the points A(-1,2,3), B(2,-2,1), and C(3,1,2), determine a vector that is perpendicular to both vec AB and vec BC. They have the solution as well showing: AB = (2,-2,1)-(-1,2,3) --- on this line, why do they decide to subtract the 2...
7. ### Significance of the Cross Product

This question is a bit philosophical. I have been reviewing the cross product, and I have a few things fresh in my mind. I know how to calculate it. I know that it always produces an output vector orthogonal to the two input vectors, and why. I also know its geometric interpretation as a...
8. ### Proof that Cross Product is not Associative using the definition of Cross Product

Does this work as a direct proof? If the cross product is associative, then (A x B) x C = A x (B x C). Consider when A = B. One the left side we have: (A x A) x C = 0 x C = 0·C·sinθ·n(AxA)xC= 0, where θ is the angle between vector A and C and n(AxA)xC is the unit vector perpendicular to...
9. ### Least squares and auto and cross correlation.

I am trying to understand why auto and cross correlation helps find the best fit line in least squares. I have an equation as stated here: Least squares - Wikipedia, the free encyclopedia I can solve and use the equation but I am trying to figure out why cross and auto correlation helps...
10. ### Meaning of these cross products

$({\bf i} + {\bf j}) \times ({\bf i} - {\bf j})=\langle 0,0,-2 \rangle$ what does this cross product show? And $({\bf i} \times {\bf j}) \times {\bf k}=\langle 0,0,0 \rangle$. Can I say that the implications of this cross product is that a vector that is perpendicular to the three other, each...
11. ### Can some one help me imagine this cross section?

Hello, I am trying to come up with the equation of the area of the triangle to find the volume of the shape, but I am having a hard time imagining it as described. Any help is appreciated. Thank you.
12. ### cross product

if given two vectors that are parallel how can you find an orthogonal vector? the cross product is the zero vector.
13. ### Cross product of two vector

I have to find the cross product of these vectors. a=<t,4,1/t>, b=<t^2,t^2,1> My attempt: So i used determinant method and found the cross product to be (4-t)i-0j-(t^3-4t^2)k I am wrong on this, can anyone verify what i have done wrong?
14. ### Vector cross product, del show that and divergence theorem

Okay, this is what I got: even if you try to work backwards surely if you do matrix 1 - matrix 2 you get zero for the middle row of the resulting matrix?
15. ### Cross - Over Trials

Hi all, I was wondering if anyone could please give me any help with any of this question? I've managed to do the rest of the paper which is mostly calculation, but this last question is very theoretical and it has me stumped! All help is appreciated! I have taken a picture of the questions...
16. ### Cross - Over Trials

Apologies, posted in the wrong section!
17. ### Determinants as scalings factors and cross products

In two dimensions, it is easy to explain why the determinant of a linear transformation works as a scaling factor of parallellograms, by showing that the formula is the same as the cross product. Likewise, for three dimensions, the determinant could be shown to be a scaling factor by showing...
18. ### At what point does this parametric curve cross itself?

Problem:The parametric curve r = (–t^2 – 4t – 4, –3cos(πt), t^3 – 28t) crosses itself at one and only one point P.a) What are the coordinates of this point P?b) Letting θ be the acute angle between the two tangent lines to the curve at the crossing point, what is the value of cos(θ)?Answers:a)...
19. ### Vectors and properties of cross products

The problem that I am unsure about is: k x (i - 2j). What are the rules for adding and subtracting vectors like this?
20. ### Cross product - non commutative algebra

In quantum mechanics I am told that the cross product of angular momentum with itself is not zero and this is because r and momentum (p) do not commute. I have \underline l = \underline r \times \underline p and \underline p = (h/i) \nabla and I want to calculate l cross l. I cannot write...