Math 242, Spring 2019, Assignment 1

By one of those caprices of the mind, which we are perhaps most subject to in early youth, I at once gave up my former occupations; set down natural history and all its progeny as a deformed and abortive creation; and entertained the greatest disdain for a would-be science, which could never even step within the threshold of real knowledge. In this mood of mind I betook myself to the mathematics, and the branches of study appertaining to that science, as being built upon secure foundations, and so, worthy of my consideration.

- Mary Shelley, Frankenstein

Read:

1. Section 12.1.
2. Section 12.2.

Carefully define the following terms, then give one example and one non-example of each:

1. Handedness (or orientation) of a coordinate system.
2. Vector.
3. Standard position (of a vector).
4. Components (of a vector).
5. Magnitude (or length) of a vector.
6. Sum (of two vectors).

Carefully state the following theorems (you do not need to prove them):

1. Distance formula in three dimensions.
2. Formula for the components of $\vec{AB}$ (in terms of the coordinates $(x_1,y_1,z_1)$ and $(x_2,y_2,z_2)$ of points $A$ and $B$).
3. Formula for the magnitude of $\vec{v}$ (in terms of its components).

Solve the following problems:

1. Section 12.1, problems 5, 7, 9, 11, 13, 17, 19, and 25-41 odd.
2. Section 12.2, problems 1, 5, 9, 13, 15, and 29.

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