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HLRGAATPreISM_35799X_14_appC

HLRGAATPreISM_35799X_14_appC - Appendix C Vectors in Space...

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Appendix C: Vectors in Space 1. The plane determined by the x -axis and the z -axis is called the xz -plane. 2. A position vector has its initial point at the origin. 3. The component form of the position vector with terminal point is . 4. The form of the position vector with terminal point is . 5. 6. 7. 8. 9. 10. 11. ; 12. ; 13. ; 14. ; 15. ; 16. ; 17. ; is the opposite of . That is . 18. The distance between points P and Q and the magnitude of are the same number. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. u u 1 2 21 2 2 1 4 21 4 2 1 7 21 7 2 69 v v 1 3 21 3 2 1 5 21 5 2 1 2 21 2 2 38 u w 1 2 21 4 2 1 4 21 3 2 1 7 21 6 2 46 v w 1 3 21 4 2 1 5 21 3 2 1 2 21 6 2 39 1 0 2 v 0 2 1 6 2 2 10 2 4 2 2 152 2 2 38 2 v 2 1 3 2 i 2 1 5 2 j 2 1 2 2 k 6 i 10 j 4 k 1 0 w u 0 2 6 2 1 2 1 2 2 38 w u 1 4 2 2 i 11 3 2 4 2 j 11 6 2 7 2 k 6 i j k 0 w 0 2 4 2 1 3 2 2 1 6 2 2 2 61 0 u 0 2 2 2 4 2 7 2 2 69 v 3 u 3 1 1 3 2 3 1 2 2 4 i 3 1 1 5 2 3 1 4 2 4 j 3 1 1 2 2 3 1 7 2 4 k 9 i 7 j 19 k 4 u 5 v 3 4 1 2 2 5 1 3 2 4 i 3 4 1 4 2 5 1 5 2 4 j 3 4 1 7 2 5 1 2 2 4 k 7 i 41 j 38 k v w 1 3 4 2 i 1 5 1 3 22 j 1 2 1 6 22 k i 2 j 4 k u w 1 2 4 2 i 1 4 1 3 22 j 1 7 1 6 22 k 2 i 7 j 13 k PQ QP PQ PQ QP QP H1 0 2 2 , 1 0 1 2 22 , 1 0 5 2I H 2, 2, 5 I 16 i 6 j 9 k PQ H1 2 14 2 , 1 4 10 2 , 1 9 18 2I H 16, 6, 9 I 15 i 20 j 10 k PQ H1 5 20 2 , 1 5 25 2 , 1 16 6 2I H 15, 20, 10 I 3 i 3 j 6 k PQ H1 3 0 2 , 1 7 4 2 , 1
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