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2001Exam2

# 2001Exam2 - EXAM II Math 51 Spring 2001 You have 2 hours No...

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EXAM II Math 51, Spring 2001. You have 2 hours. No notes, no books. YOU MUST SHOW ALL WORK AND EXPLAIN ALL REASONING TO RECEIVE CREDIT Good luck! Name ID number 1. (/20 points) 2. (/20 points) 3. (/20 points) 4. (/20 points) 5. (/20 points) Bonus (/10 points) Total (/100 points) “On my honor, I have neither given nor received any aid on this examination. I have furthermore abided by all other aspects of the honor code with respect to this examination.” Signature: Circle your TA’s name: Kuan Ju Liu (2 and 6) Robert Sussland (3 and 7) Hunter Tart (4 and 8) Alex Meadows (10) Dana Rowland (11) Circle your section meeting time: 11:00am 1:15pm 7pm 1

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1. (a) Use determinants to find the area of the triangle in R 2 with vertices located at 1 5 , 4 3 , - 2 1 (b) Use the cross product to determine the area of the triangle in R 3 with vertices located at 1 2 4 , 2 5 3 , 0 - 4 2 2
(c) Noticing that for vectors -→ v , -→ w , and -→ x , we have ( -→ v × -→ w ) · -→ x = det x 1 x 2 x 3 v 1 v 2 v 3 w 1 w 2 w 3 use the properties of the determinant to show that the cross product of two vectors is always perpendicular to each of those two vectors.

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