Question 1076191
So the scalar projection of u onto v is,
{{{S=(v*u)/abs(v)=(6(-5)+7(-1))/sqrt(5^2+1^2)=(-30-7)/sqrt(26)=-37/sqrt(26)}}}
Now just multiply by the unit vector in the v direction.
{{{V[unit]}}}=({{{-5/sqrt(26)}}},{{{-1/sqrt(26)}}})
So then,
{{{u[v]}}}=({{{(-37/sqrt(26))(-5/sqrt(26))}}},{{{(-37/sqrt(26))(-1/sqrt(26))}}})
{{{u[v]}}}=({{{185/26}}},{{{37/26}}}
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u=6(1,0)+7(0,1)
(1,0) and (0,1) are orthogonal since their dot product equals zero.
{{{1*0+0*1=0}}}