Define, for continuous functions f$($x$)$ and g$($x$),$ an inner product

$=$

$1$f$($x$)$g$($x$)$dx$1$

$.$

$(1)$ Are the functions f$($x$)=$ ex$2$ and g$($x$)=$ sin x orthogonal to each other? $($Write Yes, or No$)$

$(2)$ The length of f$($x$)=$ x is