Scalars and Vectors Practice Questions
Review these concepts at: Scalars and Vectors Study Guide
- 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?
- Calculate the magnitude of vector C in problem 12.
- 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.
A2 = A2x + A2y + A2z
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