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proj_week3

# proj_week3 - P =(1 2 3 and the line x = 8-2 t y =-5 t z =-4...

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MAT 267 Richard Reynolds; No TI-89s or TI 92s 1 1) A) Find a vector equation of the line through the point (3, 2, 1) that is normal to the plane 2 x - y + 3 z = - 21 . B) Find the value of t where the above line intersects the given plane. C) Find the point on the plane where the above line intersects the given plane. D) Use (C) to find the distance from the point (3,2,1) to the plane 2 x - y + 3 z = - 21 .

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MAT 267 Richard Reynolds; No TI-89s or TI 92s 2 2) For the point
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Unformatted text preview: P = (1 , 2 , 3) and the line x = 8-2 t , y =-5 + t , z =-4 + 3 t ; A) Find the distance between P and an arbitrary point on the line, in terms of the parameter t . B) Find the value of t that minimizes the distance function above (Hint: minimize d 2 ). C) Find the point on the line that is closest to P . D) Use (C) to ﬁnd the distance the point (1, 2, 3) is to the line r ( t ) = h 8-2 t,-5 + t,-4 + 3 t i...
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