WI21 10C Exam 1 key.pdf - 2021 Winter Math 10C Exam 1(You...

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2021 Winter Math 10C Exam 1 (You must show your work) Name: Section: 1. [20pts] Consider three points P (1 1 3) Q (2 3 5) R ( 3 2 1) . (a) [15pts] Find a unit vector orthogonal to the plane containing P Q R whose -coordinate is positive. (b) [5pts] Find an area of the triangle with vertices P Q and R . 2. [10pts] Determine if the vectors u = 0 1 2 v = 1 2 3 and w = 2 3 4 are co-planar. (You must show this algebraically. Do not use a graph.) 3. [10pts] Determine if the lines L 1 and L 2 are parallel, skew or intersecting. If intersect, find the intersection. (You must show this algebraically. Do not use a graph.) (a) [5pts] L 1 : u 1 + v 1 and L 2 : u 2 + v 2 where u 1 = (1 2 3) v 1 = ( 2 1 2) u 2 = (3 7 5) and v 2 = ( 3 3 2 3) . (b) [5pts] L 1 : 2 = 2 3 = +2 4 and L 2 : +1 5 = +1 2 = 2 5 4 . 4. [10pts] Determine if two vectors are orthogonal, parallel or neither.

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