the temperature T at a surface is given by T=x²+y²-z. in which direction a mosquito at point (4,4,2) on the surface

will fly so that it cools fastest.

a)8i+8j-k

b)-8i-8j+k

c)i-j+2k

d)i+j-k

plz solve in detail

i think the ans shud be 'b'....am i correct??

well...i did it this way.....

the temp gradient will be...T/x  + T/y  + T/z  

=2x +2y -

now this is the direction in which max increase in the temp takes place.......

hence fr the fly to cool faster it shud move in the opp direction ie in the direction of  -2x -2y +......

sub the pt n ull get the ans as 'b'