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Paul
August 7, 2018

Calculus II - Assignment Problems
 Series & Sequences Previous Chapter Next Chapter 3-Dimensional Space Vector Arithmetic Previous Section Next Section Cross Product

Dot Product

For problems 1  5 determine the dot product, .

1. ,

2.  ,

3.  ,

4. ,  and  the angle between the two vectors is  .

5. ,  and  the angle between the two vectors is  .

For problems 6  8 determine the angle between the two vectors.

6. ,

7. ,

8. ,

For problems 9  12 determine if the two vectors are parallel, orthogonal or neither.

9. ,

10. ,

11. ,

12. ,

13. Given that ,  and the angle between  and  is  determine if  is a unit vector or note.

For problems 14 & 15 determine the value of b for which the two vectors will be orthogonal.

14. ,

15. ,

16. Given  and  compute .

17. Given  and  compute .

18. Given  and  compute .

19. Given  and  compute

20. Determine the direction cosines and direction angles for

21. Determine the direction cosines and direction angles for .

22. Prove the property .

23. Prove the property .

24. Prove the property .

25. Prove the property .

 Vector Arithmetic Previous Section Next Section Cross Product Series & Sequences Previous Chapter Next Chapter 3-Dimensional Space

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