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**Unformatted text preview: **Math 103 section 1 - Exam 1 Instructions: • You are not permitted to use a calculator or any other materials on this exam. • Show all your work on the test. You may use the back of the pages if needed. • Simplify all answers. Give exact answers (i.e. fractions, radicals, etc.) unless instructed otherwise. • Sign the Honor Pledge after you finish the exam. I have neither given nor received any unauthorized help on this test, and I have conducted myself within the guidelines of the university honor code. Name and section: Pledge: Question: 1 2 3 4 5 6 7 8 Total Points: 21 5 12 10 6 10 14 6 84 Score: 1. (21 points) Given the points P (1 , 1 , 1), Q (2 , 2 , 3), R (1 , 2 , 3), S (2 , 1 , 4). (a) Compute the angle between ~ PQ and ~ PS . Solution: ~ PQ = h 1 , 1 , 2 i and ~ PS = h 1 , , 3 i So, θ = cos- 1 (1+6) √ 1+1+4 √ 1+9 = cos- 1 7 2 √ 15 (b) Give the equation of the plane containing the points P , Q , and S . Solution: n = ~ PQ × ~ PS = i j k 1 1 2 1 0 3 = h 3 ,- 1 ,- 1 i So, the equation of the plane is 3( x- 1)- ( y- 1)- ( z- 1) = 0 or simplified: 3 x- y- z = 1 (c) Find the symmetric equations of the line perpendicular to the plane through P,Q,S which passes thru R . Solution: Direction of the line will be n as computed above....

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