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hi

ok.

@mathstina what is the gradient vector for any point on the sphere?

what is point ? is it (0,0,0)?

what do i sub for r value?

2x i + 2y j + 2z k = r^2

r is a constant for a sphere, so this thingy should be =0

grad f=2x i + 2y j + 2z k = 0
still with me?

yes

(a,b,c)?

yes, and what is the gradient at that point ?

is it find the parametric eqn?

a picture may help us visualize what we're doing|dw:1352129016463:dw|

2a i+2b j+2c k =0

multiplied by 2

yes, so what does that say bout the relationship between the two vectors?

sry, im nt sure

positive gradient

both pointing in the same dirn; parallel

yes, now look at what this means visually...

|dw:1352129640330:dw|

the points are on the level surface

hence all normal lines to the surface pass through the origin*

yes.

good, then we're done :)

ihw do i answer the qn? mathematically written