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# Practice Assignment.pdf

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School
University of Waterloo
Department
Mathematics
Course
MATH 124
Professor
Misc
Semester
Winter

Description
MATH 124 - PRACTICE ASSIGNMENT NOTE: This assignment is for practice only, it is not due. 1.Determine: (a) proj (1;▯2;1)5;1;▯2) and perp (1;▯2;1)5;1;▯2) (b) proj (0;1;▯1)4;4;2) and perp (0;1;▯1)4;4;2) (c) proj (1;0;▯1)6;2;6) and perp (1;0;▯1)6;2;6) (d) proj (▯1;2;▯1;2) and perp (▯1;2;▯1;2) (2;0;1;1) (2;0;1;1) 2.Find the distance from the point to the line in each case. Also ▯nd the point on the line that is closest to the given point: (a) point (3;▯5), line (2;▯4) + t(3;▯4) where t 2 R (b) point (0;0;2), line (2;1;0) + t(▯1;2;2) where t 2 R (c) point (1;▯3;0), line (1;▯1;▯1) + t(1;1;1) where t 2 R (d) point (▯1;2;▯3), line (4;1;▯2) + t(2;1;4) where t 2 R 3.Find the distance from the point to the plane. Also ▯nd the point on the plane closest to the given point. (a) point (2;▯3;▯1), plane 2x ▯ 1x ▯ 5x2= 7 3 (b) point (2;2;3), plane 2x + x ▯ 4x = 5 1 2 3 (c) point (2;▯1;2), plane
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