<s>[INST] maximum value of the expression : $2x+3y+z$ as $(x,y,z)$ varies over the sphere $x^2+y^2+z^2=1$ I have to find out the maximum value of the expression :


$2x+3y+z$ as $(x,y,z)$ varies over the sphere $x^2+y^2+z^2=1.$


 [/INST] By Cauchy Schwarz inequality $$(2x+3y+z)^2\le (4+9+1)(x^2+y^2+z^2)$$
$\therefore$ the maxium value that  can be attained is when $2x=3y=z$ , and the value attained is $\sqrt{14}$
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