Multi-part question involving a vector field

Click For Summary
SUMMARY

The discussion revolves around the evaluation of a vector field, specifically ##\vec G=24xy\hat a_x+12(x^2+2)\hat a_y+18z^2\hat a_z##, at points P(1,2,-1) and Q(-2,1,3). The participants calculate the vector field values at these points, correcting arithmetic errors and discussing the concept of unit vectors. The conversation emphasizes the distinction between evaluating a vector field and constructing displacement vectors between points, ultimately leading to the calculation of unit vectors from Q to P.

PREREQUISITES
  • Understanding of vector fields and their properties
  • Familiarity with unit vectors and their calculation
  • Proficiency in vector arithmetic and notation
  • Basic knowledge of calculus and vector calculus concepts
NEXT STEPS
  • Study the concept of vector fields in depth, focusing on examples like wind velocity and electric fields.
  • Learn how to compute unit vectors from arbitrary vectors in various contexts.
  • Explore the application of vector fields in physics, particularly in electrodynamics.
  • Practice vector arithmetic and notation through exercises involving multiple points in space.
USEFUL FOR

Students and professionals in physics, mathematics, and engineering who are working with vector fields, as well as educators teaching these concepts.

  • #31
CaliforniaRoll88 said:
Is that compatible with windows?
I don’t think so.
 
  • Like
Likes   Reactions: CaliforniaRoll88
Physics news on Phys.org
  • #32
CaliforniaRoll88 said:
Part d)
##\vec G=24xy\hat a_x+12(x^2+2)\hat a_y+18z^2\hat a_z##
##60^2=(24xy)^2+[12(x^2+2)]^2+(18z^2)^2##
##60^2=24^2x^2y^2+[12x^2+24]^2+18^2z^4##
##60^2=24^2x^2y^2+12^2x^4+2(12x^2)(24)+24^2+18^2z^4##
##60^2=24^2x^2y^2+12^2x^4+24^2x^2+24^2+18^2z^4##
##60^2=6^2[4^2x^2y^2+2^2x^4+4^2x^2+4^2+3^2z^4]##
##100=4x^4+16x^2+16x^2y^2+9z^4+16##
Here is the surface above. It's a bit different from mine but, like I said, I'm learning how to do this.

 
  • Like
Likes   Reactions: CaliforniaRoll88
  • #33
That's awesome. I have my own surface XD. Thank you.
 
Last edited:
  • Like
Likes   Reactions: PeroK

Similar threads

Replies
2
Views
1K
Replies
2
Views
2K
  • · Replies 4 ·
Replies
4
Views
1K
  • · Replies 11 ·
Replies
11
Views
1K
  • · Replies 5 ·
Replies
5
Views
1K
Replies
3
Views
3K
Replies
1
Views
3K
  • · Replies 3 ·
Replies
3
Views
1K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K