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Calculus II (Assignment Problems) / Vectors / Dot Product   [Notes] [Practice Problems] [Assignment Problems]

Calculus II - Assignment Problems
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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

Calculus II (Assignment Problems) / Vectors / Dot Product    [Notes] [Practice Problems] [Assignment Problems]

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