By Valentina Tobos | Laurentiu Tobos

Updated on Sep 26, 2011

Review these concepts at: Scalars and Vectors Study Guide

**Practice Questions**

- Find the polar coordinates
*r*and*θ*of a point*P*having Cartesian coordinates*x*= 3 and*y*= 6. - What is the distance between point
*P*having Cartesian coordinates (2,5) and point*Q*having coordinates (5,9)? - What are the polar coordinates of point
*Q*in the previous question? - What angle does the segment
*PQ*make with the axis*Ox*in the previous question? - What is the distance from the origin to point
*Q*in practice problem 2? - A point
*P*has the following coordinates in a cylindrical system: (3,30°,5). Find the coordinates in a Cartesian 3-D system. - What is the distance from point
*P*to the origin in practice problem 6? - A point
*P*in a horizontal plane has coordinates (–3.50,6.20) meters. Find the polar coordinates of this point. - Find the magnitude of the following vectors: (3.0,–5.0,6.0) meters and (20,45,–30) N.
- Is it possible for a vector to have zero magnitude but nonzero components? Explain
- In Figure 2.12, which vectors are equal? Explain.
- Let
**A**= 2.0**i**+ 3.0**j**and*B*= 3.0**i**–2.0**j**. Using the properties of unit vectors**i**,**j**, and**k**, find the components of the vector**C**=**A**×**B**. - Calculate
**A**·**B**for the vectors in problem 12. What can you say about the directions of**A**and**B**? - Calculate
**A**·**C**and**B**·**C**for the vectors in problem 12. What can you say about their directions? - For the vectors in problem 12, calculate
**A**+**B**and**B**–**A**. What are the magnitudes of these two new vectors? - What can you say about the directions of the vectors calculated in problem 15?
**C**in problem 12.
Calculate the magnitude of vector

**Answers**

*r*= 6.71,*θ*= 63.4°*PQ*= 5*r*= 10.3,*θ*= 60.94°*θ*= 53.13°*OQ*= 10.3*x*= 2.598,*y*= 1.5,*z*= 5*OP*= 5.83*r*= 7.12,*θ*= 119.445°- 8.37 m and 57.66 N
- No, see relation for magnitude:
*A*=*F**C*= –13*k**A*·*B*= 0; therefore, the vector's directions are perpendicular to each other.- Same as for problem 13
*A*+*B*= 5.0 i + 1.0 j and*B*–*A*= 1.0 i – 5.0 j. Both magnitudes equal 5.1.- The directions are perpendicular, as the scalar product of the vectors is zero.
- The magnitude is 13.

*A*^{2} = *A*^{2}_{x} + *A*^{2}_{y} + *A*^{2}_{z}

From Physics Success in 20 Minutes A Day. Copyright © 2006 by LearningExpress, LLC. All Rights Reserved.

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