Expression 9: "B" Subscript, 2 , Baseline equals left parenthesis, "B" Subscript, 1 , Baseline . "x" negative "A" Subscript, 1 , Baseline . "x" , "B" Subscript, 1 , Baseline . "y" negative "A" Subscript, 1 , Baseline . "y" , "B" Subscript, 1 , Baseline . "z" , right parenthesisB2=B1.x−A1.x,B1.y−A1.y,B1.z
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Expression 10: "u" Subscript, 2 , Baseline equals vector left parenthesis, "A" Subscript, 2 , Baseline , "B" Subscript, 2 , Baseline , right parenthesisu2=vectorA2,B2
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To see what is happening, let's view in 2D (hit 2D plane icon in right corner) - and then come back to 3D (hit the 3D space icon )
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Next we need to move u_2 in the z-direction as to start at a point whose x-value is 0. So mess with the z-coordinate but keep x and y coordinate the same.
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Expression 13: "A" Subscript, 3 , Baseline equals left parenthesis, "A" Subscript, 2 , Baseline . "x" , "A" Subscript, 2 , Baseline . "y" , "A" Subscript, 2 , Baseline . "z" negative "A" Subscript, 2 , Baseline . "z" , right parenthesisA3=A2.x,A2.y,A2.z−A2.z
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Expression 14: "B" Subscript, 3 , Baseline equals left parenthesis, "B" Subscript, 2 , Baseline . "x" , "B" Subscript, 2 , Baseline . "y" , "B" Subscript, 2 , Baseline . "z" minus "A" Subscript, 2 , Baseline . "z" , right parenthesisB3=B2.x,B2.y,B2.z−A2.z
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Expression 15: vector left parenthesis, "A" Subscript, 3 , Baseline , "B" Subscript, 3 , Baseline , right parenthesisvectorA3,B3
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Take away: The vector from the point A=(x_A,y_A , z_A) to the point B=(x_B,y_B, z_B) is equal to the vector from the origin (0,0),0 to the point (x_B - x_A , y_B - y_A, z_B - z_A).
