#$2)$ In scientific and big$-$data applications, it's common to group a long list

of data into a 'vector', such as the following':

user$1=(0\mathrm{.}1,0\mathrm{.}2,0\mathrm{.}3,0\mathrm{.}25,0\mathrm{.}59,0\mathrm{.}7,0\mathrm{.}99,0\mathrm{.}85,0\mathrm{.}01,0\mathrm{.}2)$

user$2=(0\mathrm{.}03,0\mathrm{.}4,0\mathrm{.}31,0\mathrm{.}22,0\mathrm{.}88,0\mathrm{.}11,0\mathrm{.}5,0\mathrm{.}87,0\mathrm{.}12,0\mathrm{.}4)$

Often, we'd like to compare how similar two of these datasets are $($for

instance, serving advertisements to two 'similar' users; or searching a

genome for two 'similar' sequences; etc$).$

We define cosine distance between two vectors a and $b$ as follows:

distance$(a,b)=1-\frac{a*b}{||a||||b||},$ where $*$ is the dot product

Compute the cosine distance between user $1$ and user$2,$ above.

This problem probably requires a calculator, and for this problem you may

$($probably should$)$ give decimal answers; also, show the intermediate

values of $a*b,||a||,||b||,$ but you don't need to manually show the whole

summation. $($Make sure you input things correctly, though.$)$