Question 1173622
<pre>
The dot product of two vectors is defined as

<b>u&#xb7;v</b> = |<b>u</b>||<b>v</b>|cos(&theta;)


and the dot product also happens to be the sum of products of corresponding components:

<b>u&#xb7;v</b> = {{{u[x]v[x] + u[y]v[y]}}}  

So we have all that is needed to solve for &theta;:


|<b>u</b>| = {{{ sqrt((-10)^2 + (-5)^2) }}} = {{{ sqrt(125) }}} = {{{ 5sqrt(5) }}}
|<b>v</b>| = {{{ sqrt((-6)^2 + 3^2) }}} = {{{ sqrt(45) }}} = {{{ 3sqrt(5) }}}

and
{{{ u[x]v[x] + u[y]v[y]}}} = {{{ (-10)(-6) + (-5)(3) }}} = {{{ 45 }}}


Putting it all together:

  {{{5sqrt(5)*3sqrt(5)*cos(theta) }}} = {{{45 }}}
  {{{75 cos(theta) }}} = {{{45 }}}
   cos(&theta;) = {{{45/75 }}}     

       &theta; = {{{cos^-1(45/75) }}} = {{{highlight( 53.13^o ) }}}