with(linalg):

Warning, the protected names norm and trace have been redefined and unprotected

u1:=[1,2,3];

NiM+SSN1MUc2IjclIiIiIiIjIiIk

u2:=[-2,1,0];

NiM+SSN1Mkc2IjclISIjIiIiIiIh

dotprod(u1,u2);

NiMiIiE=

v:=[0,4,2];

NiM+SSJ2RzYiNyUiIiEiIiUiIiM=

normsq:=proc(w) w[1]^2+w[2]^2+w[3]^2 end;

NiM+SSdub3Jtc3FHNiJmKjYjSSJ3R0YlRiVGJUYlLCgqJCY5JDYjIiIiIiIjRi4qJCZGLDYjRi9GL0YuKiQmRiw2IyIiJEYvRi5GJUYlRiU=

normsq(u1);

NiMiIzk=

normsq(u2);

NiMiIiY=

dotpr:=proc(w,ww) w[1]*ww[1]+w[2]*ww[2]+w[3]*ww[3] end;

NiM+SSZkb3Rwckc2ImYqNiRJIndHRiVJI3d3R0YlRiVGJUYlLCgqJiY5JDYjIiIiRi8mOSVGLkYvRi8qJiZGLTYjIiIjRi8mRjFGNEYvRi8qJiZGLTYjIiIkRi8mRjFGOUYvRi9GJUYlRiU=

dotpr(v,u1);

NiMiIzk=

dotpr(v,u2);

NiMiIiU=

ProjOfVOnU1:=dotpr(v,u1)/normsq(u1)*u1 ;

NiM+SSxQcm9qT2ZWT25VMUc2IjclIiIiIiIjIiIk

ProjOfVOnU2:= dotpr(v,u2)/normsq(u2)*u2;

NiM+SSxQcm9qT2ZWT25VMkc2IjclIyEiKSIiJiMiIiVGKSIiIQ==

ProjOfVOnU:=ProjOfVOnU1 + ProjOfVOnU2;

NiM+SStQcm9qT2ZWT25VRzYiNyUjISIkIiImIyIjOUYpIiIk

As a test of whether the orthogonal projection above really "pulls everything U-like from v", let's check that the remaining part of v is orthogonal to U; that is, check that v-(ProjOfVOnU) is orthogonal to both u1 and u2.N:=v-ProjOfVOnU;

NiM+SSJORzYiNyUjIiIkIiImIyIiJ0YpISIi

dotpr(N,u1);

NiMiIiE=

dotpr(N,u2);

NiMiIiE=

Now let's see what the geometry looks like.with(plots):SubspaceU:=plot3d(expand(s*u1+t*u2), s=-1..5, t=-1..5, grid=[5,5]):display(SubspaceU);

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

VectorU1:=tubeplot(expand(t*u1), t=0..3, radius=.3, numpoints=6):VectorU2:=tubeplot(expand(t*u2), t=0..3, radius=.3, numpoints=5):display({SubspaceU, VectorU1, VectorU2}, axes=normal);

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

VectorV:=tubeplot(expand(t*v), t=0..3, radius=.3, numpoints=4, color=blue):display({SubspaceU, VectorU1, VectorU2, VectorV}, axes=normal);

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VectorProjV:=tubeplot(expand(t*ProjOfVOnU), t=0..3, radius=.3, numpoints=4, color=turquoise):display({SubspaceU, VectorU1, VectorU2, VectorV, VectorProjV}, axes=normal);

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VectorN:=tubeplot(expand(t*N+3*ProjOfVOnU), t=0..3, radius=.3, numpoints=4, color=pink):display({SubspaceU, VectorU1, VectorU2, VectorV, VectorProjV, VectorN}, axes=normal);

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