assig2 - x-2 y + 3 z = 1. (a) What is the normal direction...

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Math 152, Spring 2010 Assignment #2 Notes: Each question is worth 5 marks. Due in class: Monday, January 18 for MWF sections; Tuesday, January 19 for TTh sections. Solutions will be posted Tuesday, January 19 in the afternoon. No late assignments will be accepted. 1. Use the definition to find the determinant of the matrix 2 2 2 1 2 3 3 0 - 3 . Do the computation by hand showing your work, but you can check your result using MATLAB. From your result, decide if the vectors [2 2 2], [1 2 3] and [3 0 -3] lie in the same plane (justify your answer, very briefly). 2. Consider the plane
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Unformatted text preview: x-2 y + 3 z = 1. (a) What is the normal direction to the plane? (b) Find the coordinates of any point (your choice) on the plane. 3. Find the intersection point of the line with parametric form below (1 , , 1) + t (1 , 2 , 3) and the plane x + 2 y-3 z = 5 . 4. The planes x + 2 y-3 z = 2 and x-2 y + 3 z = 7 intersect in a line. Find a parametric representation of this line. 5. Consider the plane P dened by x-2 y + 3 z = 1. (a) Show that the point (1,2,3) is not on the plane P . (b) Find the point on P that is the closest to (1,2,3)....
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