Adding spatial 3-vectors

Add3[A_, B_] := Plus[A, B]

Add3[a3, b3]//MatrixForm

( {{a0 + b0}, {{ax + bx, ay + by, az + bz}}, {{aix + bix, aiy + biy, aiz + biz}}, {ai + bi}} )

Add3[a3v, b3v]//MatrixForm

( {{0}, {{ax + bx, ay + by, az + bz}}, {{0, 0, 0}}, {0}} )

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