calculation

[Wesleytoddy]

Given a point P0 = (x0, y0, z0) and a surface of equation g (x, y, z) = 0, show that the point P = (x, y, z) of the surface, which is the critical point of the square
of the distance from P to P0 is such that the direction of the vector - → P0P coincides with the direction of the gradient of g in P.

 

[Otis]

Hello Wesley. Have you started anything, yet? Are there any parts of the exercise statement that are unclear? Tutors would like to see where you're at.

Please check out the forum's submission guidelines, too. Thanks!

?

 

[Wesleytoddy]

I really do not know where to start for problem solving

 

[Deleted member 4993]

Given a point P0 = (x0, y0, z0) and a surface of equation g (x, y, z) = 0, show that the point P = (x, y, z) of the surface, which is the critical point of the square
of the distance from P to P0 is such that the direction of the vector - → P0P coincides with the direction of the gradient of g in P.

Can you please tell us the definition of:

The gradient of the surface in mathematical terms?

 

[ksdhart2]

Well, I find that 95% of the time when students claim they "have no idea" where to start, they're being hyperbolic and overdramatic, and they really do have some idea where to start. However, for now I will take you at face value and assume you're being literal. The best place to start any problem is to be sure you know what the terms in the problem text mean.

• Do you know what points, line, and planes are?
• Do you know a formula to find the distance between two points?
• Do you know what a vector is?
• More specifically, do you know what a gradient vector is?
• As Subhotosh Khan asks, do you know how to find the gradient of a surface?
• Do you know how to determine if two vectors have the same direction?
• Finally, do you know what the sentence "the point P = (x, y, z) of [on?] the surface which is the critical point of the square of the distance from P to P0" means? (Because I sure don't!)