Next move vector u_2 in the y-direction as to start at a point whose y-value is 0. So mess with the y-coordinate but keep x-coordinate the same.
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Expression 14: vector left parenthesis, "A" Subscript, 2 , Baseline , "A" Subscript, 3 , Baseline , right parenthesisvectorA2,A3
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Expression 15: "A" Subscript, 3 , Baseline equals left parenthesis, "A" Subscript, 2 , Baseline . "x" , "A" Subscript, 2 , Baseline . "y" negative "A" Subscript, 2 , Baseline . "y" , right parenthesisA3=A2.x,A2.y−A2.y
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Expression 16: vector left parenthesis, "B" Subscript, 2 , Baseline , "B" Subscript, 3 , Baseline , right parenthesisvectorB2,B3
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Expression 17: "B" Subscript, 3 , Baseline equals left parenthesis, "B" Subscript, 2 , Baseline . "x" , "B" Subscript, 2 , Baseline . "y" minus "A" Subscript, 2 , Baseline . "y" , right parenthesisB3=B2.x,B2.y−A2.y
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Expression 18: "u" Subscript, 3 , Baseline equals vector left parenthesis, "A" Subscript, 3 , Baseline , "B" Subscript, 3 , Baseline , right parenthesisu3=vectorA3,B3
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Note you can think of moving the green vector to the purple vector, keeping it the same vector (so keeping the same length and direction) by moving the green vector to the purple vector by the arrows indicated in below orange vectors.
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Expression 20: vector left parenthesis, "A" Subscript, 1 , Baseline , "A" Subscript, 3 , Baseline , right parenthesisvectorA1,A3
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Expression 21: vector left parenthesis, "B" Subscript, 1 , Baseline , "B" Subscript, 3 , Baseline , right parenthesisvectorB1,B3
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Take away: The vector from the point A=(x_A, y_A) to the point B=(x_B,y_B) is equal to the vector from the origin (0,0) to the point (x_B - x_A , y_B - y_A).
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To prepare for the next example, let's veiw this example in 3D (hit the 3D "box" icon in upper right cornor).
