For a geometric understand, let's use the "head-to-tail method" to add vectors. Let's move vector purple v so that it starts where vector blue u ends.
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Expression 15: vector left parenthesis, "U" , "V" Subscript, 2 , Baseline , right parenthesisvectorU,V2
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Expression 16: "V" Subscript, 2 , Baseline equals left parenthesis, "V" . "x" negative "O" . "x" positive "U" . "x" , "V" . "y" negative "O" . "y" positive "U" . "y" , right parenthesisV2=V.x−O.x+U.x,V.y−O.y+U.y
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Now for the vector u minus the vector v
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Expression 18: "v" Subscript, "n" , Baseline equals negative "v"vn=−v
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Expression 19: "V" Subscript, "n" , Baseline equals left parenthesis, negative "V" . "x" , negative "V" . "y" , right parenthesisVn=−V.x,−V.y
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Expression 20: "u" minus "v"u−v
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For an geometric understanding, let's use the "head-to-tail method" to add vectors. So move the green vector -v so that it starts where blue vector u ends.
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Expression 22: vector left parenthesis, "U" , "V" Subscript, 3 , Baseline , right parenthesisvectorU,V3
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Expression 23: "V" Subscript, 3 , Baseline equals left parenthesis, "V" Subscript, "n" , Baseline . "x" negative "O" . "x" positive "U" . "x" , "V" Subscript, "n" , Baseline . "y" negative "O" . "y" positive "U" . "y" , right parenthesisV3=Vn.x−O.x+U.x,Vn.y−O.y+U.y
