# A difficult (for me) 3d shapes problem

• ydan87
Oh, my apologies. The cross product is a mathematical operation between two vectors that results in a third vector that is perpendicular to both original vectors. In this case, the cross product is used to show the relationship between the vector from point p to point b and the normal vector n, which determines the direction of the cylinder's axis. Does that make sense?
ydan87
If I have a cylinder with a radius r and an axis that passes through point b with the
direction of vector n, show that its equation can be written in any of the following forms:
1) ||(p-b) X n|| = r
2) (p - b) X n = r.e (where e s ia unit vector orthogonal to n)
3) ||(p-b) - ((p-b).n)n|| = r
. = vector-vector dot product
X = vector-vector cross product

Thanks in advance for any guide given...

hi ydan87!

start by translating each of 1) 2) and 3) into ordinary english …

what do you get?

Tiny tim
1) the length of the vector you get by the cross product of the vector from point p to point b and normal n equals to r, the radius of the cylinder.
2) the vector you get by the cross product above equals to the vector you get by multiplying scalar r with vector e, which is a unit vector orthogonal to n.
If you guide me through those i'll be ok with 3.

Is it clearer now?

ydan87 said:
1) the length of the vector you get by the cross product of the vector from point p to point b and normal n equals to r, the radius of the cylinder.
2) the vector you get by the cross product above equals to the vector you get by multiplying scalar r with vector e, which is a unit vector orthogonal to n.

ok

now also use the words "cos" or "sin"

Can you please explain what you mean? I can't give you the parametric representation if that's what you mean...

i meant explain what the cross product is, instead of just saying "cross product"!

## 1. What is the problem about 3d shapes?

The problem involves finding the volume of a complex 3d shape, which can be challenging for some individuals.

## 2. What skills are needed to solve this 3d shapes problem?

Solving this problem requires a strong understanding of geometry, specifically 3d shapes and their properties. It also requires the ability to visualize and manipulate 3d objects in your mind.

## 3. How can I approach solving this 3d shapes problem?

One approach is to break down the complex shape into smaller, more manageable shapes. You can then use formulas or methods to find the volume of each smaller shape and add them together to get the total volume.

## 4. Are there any tips or tricks for solving this problem?

Some tips include drawing a diagram to visualize the shape, using known formulas for common 3d shapes, and checking your work by using a different method or approach.

## 5. What real-world applications does this 3d shapes problem have?

Understanding how to find the volume of complex 3d shapes is important in fields such as architecture, engineering, and construction. It is also used in manufacturing and design to determine the amount of material needed for a product.

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