math103Exam1Sec1Solutions

# math103Exam1Sec1Solutions - Math 103 section 1 Exam 1...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

{[ snackBarMessage ]}

### Page1 / 8

math103Exam1Sec1Solutions - Math 103 section 1 Exam 1...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online