Curves and Surfaces - ME 210 Applied Mathematics for...

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ME 210 Applied Mathematics for Mechanical Engineers Prof. Dr. Faruk Arınç Spring 2010 Equations of Lines and Planes in 3-D Space Straight Lines Consider the straight line, L. passing through a given point P 1 (x 1 , y 1 , z 1 ,) and parallel to a given vector . For any point, P(x, y, z) on the straight line: 1 1 1 1 PP = t V = x - x i + y - y j + z - z k = t a i + b j + c k where t is any non-zero scalar. V = a i + b j + c k V 1 P P 1 1 1 x - x = t a y - y = t b z - z = t c are the parametric equations of the straight line, L. This can be written as 1 1 1 x - x y - y z - z = = = t a b c
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