# A 2 a 3 a 4 a 5 a 6 a 7 a 1 2 0 5 1 4 2i i

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Unformatted text preview: k, 2j (b) Use the right-hand rule to decide whether the components of a b are positive, negative, or 0. 0, 3, 1 b 2i t, t 2, t 3 , b 7. a ■ j b and verify that it is orthogonal ■ a 3k et j x e tk 13. If a 1, 2 t, 3 t 2 ■ ■ ■ ■ ■ ■ ■ ■ 1, 2, 1 14. If a 3, 1, 2 , b bc a that a 8. If a a i 2 k and b j k, ﬁnd a b. Sketch a, b, and b as vectors starting at the origin. |||| Find u v and determine whether u into the page or out of the page. 17. Show that 0 b and b a. 4 , show 0, 0, 1, 1 and b j k and 2 i 0 for any vector a in V3. 0 a b 0 for all vectors a and b in V3. 19. Prove Property 1 of Theorem 8. v is directed 20. Prove Property 2 of Theorem 8. 21. Prove Property 3 of Theorem 8. 22. Prove Property 4 of Theorem 8. 23. Find the area of the parallelogram with vertices A | v |=8 150° | v |=10 a 18. Show that a | u |=6 60° 1, 1, 0 , and c b c. 16. Find two unit vectors orthogonal to both i 11. | u |=5 0, 1, 3 , ﬁnd a 0, 4, 4 . why. If so, state whether it is a vector or a scalar. (a) a b c (b) a bc (c) a (d) a b bc c (e) a b (f) a b cd cd 10–11 and b 15. Find two unit vectors orthogonal to both 1, 9. State whether each expression is meaningful. If not, explain 10. y B 0, 4 , C 4, 2 , and D 2, 2, 1 , 1. 24. Find the area of the parallelogram with vertices K 1, 2, 3 , ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ 12. The ﬁgure shows a vector a in the xy-plane and a vector b in the direction of k. Their lengths are a (a) Find a b . 3 and b 2. ■ L 1, 3, 6 , M 3, 8, 6 , and N 3, 7, 3 . 25–28 |||| (a) Find a vector orthogonal to the plane through the points P, Q, and R, and (b) ﬁnd the area of triangle PQR. 25. P 1, 0, 0 , Q 0, 2, 0 , R 0, 0, 3 k. 5E-13(pp 848-857) 1/18/06 11:23 AM Page 857 S ECTION 13.4 THE CROSS PRODUCT 26. P 2, 1, 5 , 27. P 0, 2, 0 , 28. P 2, 0, ■ Q ■ 1, 3, 4 , Q 4, 1, 3, R 3, 0, 6 2, Q 3, 1, 0 , ■ ■ minimum values of the length of the vector u direction does u v point? R 5, 3, 1 ■ ■ ■ ■ ■ ■ ■ 29–30 |||| Find the volume of the parallelepiped determined by the vectors a, b, and c. 29. a 6, 3, 30. a ■...
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## This note was uploaded on 02/04/2010 for the course M 56435 taught by Professor Hamrick during the Fall '09 term at University of Texas at Austin.

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