TEXAS A&M UNIVERSITY DEPARTMENT OF MATHEMATICS MATH 251-507/509

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TEXAS A&M UNIVERSITY DEPARTMENT OF MATHEMATICS MATH 251-507/509 Exam 1 version A, 17 Sep 2009 On my honor, as an Aggie, I have neither given nor received unauthorized aid on this work.

Name (print): In questions 2-4, no analytical work — no points .

1.

Just give answers: 1. Is the following a vector or a scalar?

• a · ( b × c ) • ( a × b ) × c 2. Calculate a · ( b × a ).

3. Which of the following vector pairs are parallel (indicate yes or no) • h 1 , 0 , 3 i and h 3 , 0 , − 1 i , • h 2 , − 4 , 8 i and h 1 , − 2 , 4 i , • h 2 , 3 , 0 i and h− 2 , − 3 , 0 i .

2.

Find the height of the triangular pyramid with the base A (0 , 1 , 2), B (2 , − 1 , 2), C (1 , 1 , 0) and the apex (top) D (2 , 1 , 1).

3.

Find the distance from the point A (2 , 1 , 1) to the line x = − 1 + 2 t , y = 1 + t , z = 1 − t .

4.

Sketch in the 3-dimensional space (if cannot sketch, describe in words in detail): (a) y = x , (b) 2 x 2 − y 2 + z 2 = − 3, (c) x 2 + y 2 = 16.

NB: Draw and label the axes!

5.

(Bonus question) Solve Question 3 by alternative methods. Give as many methods as you can for 1 point per method (if judged sufficiently different).

Points: /20

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