Question

Hi good day I'm Joshua James A. Bravante. I'm taking up BS Mathematics minor in Statistics, from Southern Luzon State University Lucban, Quezon Philippines. I need some help for my project in Mathematical Analysis III that we need to exchange idea in particular topic. I choose vector in three dimensional . Can you help me?

Answer 1

can you be specific ? Where do you need help in 3D ?

Answer 2

specifically in rectangular coordinate system

Answer 3

Are you asking for my help ?

Answer 4

yes, please,

Answer 5

wow! Thats the first time in my life! :')

Answer 6

I'll see what I can do !

Answer 7

:'( so i am leaving

Answer 8

We need to exchange ideas about a particular topic, 3D, particularly rectangular coordinate system.

Answer 9

i think i can help u

Answer 10

Let's talk about 3 dimensional, particularly in rectangular coordinate system.
What can you say about that?

Answer 11

based on the definition of three dimensional the set of real numbers is called the three dimensional number space , denoted R cube.Each ordered triple pairs (x,y,z) is called a point in three dimensional number space.

Answer 12

Right...

Answer 13

And each vector in 3d corresponds to a point in the Cartesian space. (R cubed)

Answer 14

Yes then to represent in a geometric three dimensional , we need to consider that directed distance of a point from three mutually perpendicular plane. How about if recrangular coordinates system.?

Answer 15

I'm not sure what that question meant, but something about the 3d vectors, they're the ones with the cross-product defined on them.

Answer 16

what can you share about cross product in 3D

Answer 17

Cross product of two vectors in 3d generates a vector which is perpendicular (usually say orthogonal) to both vectors that were cross-product---ed XD
Also, cross product is not commutative, unlike dot product.

Two vectors in 3d are parallel if and only if their cross product is the zero vector.

Answer 18

Yes based on the theorem If A and B are two vectors in V sub 3, then the vector A, X, B is orthogonal to both A and B.

Answer 19

I've run short of what I know about vectors in 3d :)

Answer 20

okay, now lets move on to the next interesting topic... quadric surface, what do you know about that? :)

Answer 21

Quadric surfaces are the extension of conic sections in 2d.
They are the Ellipsoid, the Elliptic Paraboloid, Elliptic Hyperboloid (of one or two sheets)
and the Hyperbolic Paraboloid

Answer 22

how to determine the characteristics of quadric surface coresponding to a general equation?

Answer 23

I haven't memorised them, sorry :)
try this
http://en.wikipedia.org/wiki/Quadric

Answer 24

okay i will just refer to the link you had sent me... i have this topic which i want to know more about it deeply. it is all about parametric equation.

Answer 25

Well, it's when both x and y are functions of some parameter t.
x = f(t)
y = g(t)

For instance
x = 3t + 5
y = 8 - 3t

These are parametric equations for the line
y =13 - x
This can easily be seen, as you just solve for t in terms of x, and substitute, however, something more interesting...

Answer 26

x = cos t
y = sin t
It might not be intuitively obvious, but actually, these are the parametric equations for the unit circle!

Answer 27

Because
1 = cos²t + sin²t = (cos t)² + (sin t)² = x² + y ²
1 = x² + y²

Answer 28

can you decipher that for me.

Answer 29

You know that the equation of a unit circle is x² + y ² = 1
Now, parametric equations were
x = cos t
y = sin t

From the Pythagorean identities, it follows that
cos²t + sin²t = 1
Substituting x for cos t and y for sin t, we get
x² + y² = 1
Which is precisely the equation of a unit circle.

Answer 30

can you please help me?