Application of the cross product: max height of z?

In summary, the conversation discusses finding the maximum value of z so that two conduits, with diameters of 1 ft. and 2 ft., can pass without interference. The solution involves using the center lines of the conduits and a unit vector to determine the distance between them. The equations ABxCD and dot product with vector AC are used to solve for z.
  • #1
brinethery
23
0

Homework Statement



http://www.scribd.com/doc/82645310

In Figure 3-31, the lines AB and CD are the center lines of two conduits 1 ft. and 2 ft. in diameter respectively. Determine the maximum value of z so that the two may pass without interference. Conduit CD must pass under AB.

Homework Equations



ABxCD

The Attempt at a Solution



ABxCD, and then make this a unit vector. Then dot this unit vector with vector AC.

The question asks "what is the maximum height z can be...". The distance from the center to the radius of the two conduits when they're touching is going to be 1.5ft (since the diameters are 1ft and 2ft respectively). This means that I'll take the two vectors I dotted and set them equal to 1.5ft. Then I'll solve for z.

Let me know if this is wrong in any way :-)

Update:

Here is what I have so far

http://www.scribd.com/doc/82663003
 
Last edited:
Physics news on Phys.org
  • #2
I'm not sure if I did this correctly. I'm trying to solve for z, and I have two equations set up, but I'm not quite sure what to do next.
 

1. What is the cross product and how is it related to finding the max height of z?

The cross product is a mathematical operation that results in a vector perpendicular to two given vectors. This vector can be used to determine the direction and magnitude of a surface or object, making it useful in calculating maximum height or distance.

2. How does the cross product help in finding the max height of z for a given object?

By finding the cross product of two vectors, one can determine the perpendicular component of the object's motion. This perpendicular component is crucial in calculating the maximum height reached by the object in question.

3. Can the cross product be applied to any object or surface to determine its max height?

Yes, the cross product can be applied to any object or surface, as long as there are two given vectors that describe the object's motion or position. It can be used in various fields such as physics, engineering, and computer graphics.

4. Is the cross product the only method for finding max height of z?

No, there are other methods such as using equations of motion or calculus, but the cross product is a useful and straightforward method for determining the max height of z in many cases.

5. Are there any limitations to using the cross product to find max height of z?

One limitation is that the cross product can only be applied to three-dimensional objects or surfaces. It also assumes that the motion of the object is in a straight line, which may not always be the case. Additionally, it requires accurate and precise measurements of the given vectors to obtain an accurate result.

Similar threads

Application of the cross product: max height of z?
    • Introductory Physics Homework Help
Replies
4
Views
2K
I Cross Product in E_u: Explaining Gourgoulhon's Text
    • Special and General Relativity
Replies
4
Views
785
Pythagorean theorem based on cross product.
    • Linear and Abstract Algebra
Replies
4
Views
3K
Cross product of complex vectors
    • General Math
Replies
4
Views
4K
What is the Definition and Properties of a Cross Product in Vector Algebra?
    • General Math
Replies
3
Views
2K
Really fundamental cross/dot product questions
    • Calculus and Beyond Homework Help
Replies
2
Views
1K
Vectors ; specifically cross product application
    • Introductory Physics Homework Help
Replies
4
Views
4K
Gradient (dot) cross product of 2 differentiable vector functions
    • Calculus and Beyond Homework Help
Replies
1
Views
6K
Intersection of planes using cross product
    • Precalculus Mathematics Homework Help
Replies
8
Views
4K
Finding cross product of two vectors a,b
    • Introductory Physics Homework Help
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top