Question 1132636
{{{u}}}= <{{{2}}}​,{{{8}}}>, {{{v}}}=<{{{4}}}​,{{{-5}}}>

{{{proj[v]u=(u*v)/(abs(u))^2}}}*<{{{4}}}​,{{{-5}}}>


{{{u*v= 8​-40=-32}}}

{{{(abs(u))^2=(sqrt(4^2+5^2))^2=(sqrt(41))^2}}}


substitute in {{{proj[v]u=(u*v)/(abs(u))^2}}}*<{{{4}}}​,{{{-5}}}>


{{{proj[v]u}}}={{{-32/(sqrt(41))^2}}}*<{{{4}}}​,{{{-5}}}>


{{{proj[v]u}}}=({{{-32/41}}})*<{{{4​}}},{{{-5}}}>


proj[v]u=({{{-32/41)4​}}},({{{-32/41)(-5)}}})


{{{proj[v]u}}}=({{{-128/41}}}​,{{{160/41}}})