Last Updated October 17, 2011

Vector Exercises

1. What is the difference between a point and a vector?
2. How can both (2,3,4) and (5,-3,1) represent the same vector?
3. What is the position of the vectror (4,2,8)?
4. What is the displacement between point (4,5,6) and point (-3,2,-1)?
5. What is the head-to-tail rule?
6. What is do we get when we displace the point (2,5,8) by the vector (1,2,3)?
7. What is the operation in the previous question called?
8. What is the length of the vector (6, 3, 2)?
9. What is the slope of vector (3,-9)?
10. What angle does the vector (1, √2) make with the x-axis?
11. What is the vector that lies at 53.13° to the x-axis and is 5 units long?
12. What vector is twice as long as (3,6,1) and is collinear to it?
13. What vector is one unit long, but in the same direction as (6,3,2)?
14. What is the dot product of two perpendicular vectors?
15. What is the dot product of the vector (2,3,4) with itself?
16. What does $ \frac{\vec{a}\cdot\vec{b}}{|b|} $ represent ?
17. How is the cross product defined in two dimensions?
18. Compare $\vec{a}\times\vec{b}$ and $ \vec{b}\times\vec{a} $
19. What is the right-hand rule?
20. What area does $|\vec{a}\times\vec{b}| $ represent?

© Ken Power 1996-2016