Question 1043082
{{{drawing(300,300,-2,10,-6,6,grid(1),line(7,-4,0,0),circle(2,1,0.2),circle(7,-4,0.2),line(2,1,0,0))}}}
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{{{v[u]=v*(u/abs(u))=(v*u)/abs(u)=(7*2+(-4)*1)/sqrt(7^2+4^2)}}}
{{{v[u]=(14-4)/sqrt(65)}}}
{{{v[u]=10/sqrt(65)}}}
{{{v[u]=(10/65)sqrt(65)}}}
{{{v[u]=(2/13)sqrt(65)}}}
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{{{u[v]=(u*v)/abs(v)=10/sqrt(2^2+1^2)=10/sqrt(5)=2sqrt(5)}}}
So then,
{{{u[1]=u[v]=2sqrt(5)}}}
and
{{{u[1]^2+u[2]^2=7^2+(-4)^2}}}
{{{(2sqrt(5))^2+u[2]^2=65}}}
{{{20+u[2]^2=65}}}
{{{u[2]^2=45}}}
{{{u[2]=sqrt(45)}}}
{{{u[2]=3sqrt(5)}}}