Quiz - Basics of Vector Algebra

True or False: Both $\bracevert A \bracevert$ and $A$ are acceptable ways to denote the magnitude of a vector called $\overline{A}$

True or False: The coordinate system that uses x, y, and z coordinates is called the Cartesian Coordinate System

True or False: Both $\hat{a}_x$ and $\hat{x}$ are acceptable ways to denote the x-directed unit vector

True or False: The speed of a car is a vector

True or False: A dot product operation results in a vector output

True or False: The Cylindrical coordinate system is defined by x, y, and θ

True or False: The Spherical coordinate system is defined by r, θ, and ϕ

True or False: The limits of the cylindrical system coordinates are:

$0\le r \le +\infty$

$0\le \theta \le 2\pi$

$-\infty \le z \le +\infty$

The z component in the Cartesian and Cylindrical systems is the same

The r component in the Cylindrical and Spherical systems is the same

True or False: the graph below accurately plots the vector $\overline{F}=3\hat{a}_x + 2\hat{a}_y$ 

Which of the following vectors on the graph below correspond to a vector $3\hat{a}_x+4\hat{a}_y$ at $(0,0)$

What is the difference between a scalar quantity and a vector?

What are the limits of the z component of the Cartesian system?

What are the x components of the following vectors?

Given the following, what is $A+B$?

$\overline{A}=2\hat{a}_x - 3\hat{a}_y + 1\hat{a}_z,$ $\overline{B}=1\hat{a}_x + 4\hat{a}_y - 2\hat{a}_z$

Given the following, find $(\overline{A}x\overline{B})+(\overline{A} \cdot \overline{B})\overline{A}$

$\overline{A}=1\hat{a}_x + 3\hat{a}_y - 4\hat{a}_z$, $\overline{B}=3\hat{a}_x + 2\hat{a}_y + 1\hat{a}_z$

Convert the following vector into Cylindrical space

$3\hat{a}_x + 6\hat{a}_y + 2\hat{a}_z$

Convert the following vector into Spherical space

$10\hat{a}_x - 2\hat{a}_y + 5\hat{a}_z$