Unformatted text preview: product. (b) Deﬁne a vector ~ b that is given by the diﬀerence between an arbitrary point ( x, y, z ) and one of the three points that deﬁne the plane. Note that ( x, y, z ) will be in the plane deﬁned by our three points if the vector ~ b is perpendicular to ~n . Use the Solve command of Mathematica to ﬁnd the condition (equation for x , y , and z ) that satisﬁes the equation ~ b · ~n = 0. Verify that the three points satisfy the equation you ﬁnd. (c) Use your solution to ﬁnd a parametric expression for the plane in R 3 that contains the three points (1 , 1 , 2), (2 , , 0), (0 ,1 , 1). That is, ﬁnd the column matrix (vector) ~x such that ~x = ~ P + t 1 ~ b 1 + t 2 ~ b 2 , where ~x = ( x, y, z ), ~ P is a particular column matrix, and t 1 and t 2 are numbers (scalars), and where ( x, y, z ) are points in the plane deﬁned by the three points (1 , 1 , 2), (2 , , 0), (0 ,1 , 1)....
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 Fall '09
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 Chemical Engineering, Santa Barbara, Department of Chemical Engineering, David Pine

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