Question 1070967
{{{abs(abs(u))=sqrt(3^2+(-1)^2)=sqrt(9+1)=sqrt(10)}}}
{{{abs((v))=(4^2+3^2)=sqrt(16+9)=sqrt(25)=5}}}
If the angle between {{{u}}} and {{{v}}} is {{{theta}}} ,
{{{abs(abs(u))*abs(abs(v))*cos(theta)=u*v}}}
Substituting,
{{{5sqrt(10)*cos(theta)=3*4+3(-1)}}}
{{{5sqrt(10)cos(theta)=9}}}
{{{cos(theta)=9/5sqrt(10)=about0.5692}}}
When I calculate that and then apply the inverse cosine function,
I get {{{highlight(theta=55.3^o)}}} .