MAT 267
TEST 1 – REVIEW
NOTE:
Below, the Examples and the hw refer to the Examples in the textbook and the homework assigned from the
textbook.
10.1 The three dimensional coordinate system.
Know how to:
•
Find the
distance between two points (see WeBWorK #2,
Example 3) and the distance from a point to any of the
coordinate axis.
•
Find the equation of a sphere (WeBWorK #5, 6, 7, 8, 9,10 Examples 4,5,6 )
•
Sketch simple surfaces such as planes and/or cylinders. (WeBWorK #4, Examples 1, 2)
10.2
Definition of vectors.
•
Know how to perform operations with vectors both geometrically (hw
#1, 2, 3) and using components (WeBWorK #1,
Examples 1, 2, 5).
•
Know the special unit vectors
i
,
j
and
k
.
•
Be able to find unit vectors (WeBWorK #2, Example 6)
and, more generally, vectors with a given length in the direction
of a given vector (hw 18)
•
Given the coordinates of two points A and B, know how to find the components of the vector
AB
(Example 3)
•
Know how to express the components of a 2D vector in terms of its length and the angle with the positive
x
-axis (polar
form).
•
Practice on application problems with force and velocity
(WeBWorK #3, 4, 5, Example 7).
10.3 The dot product.
•
Know the definition(s) (WeBWorK 1, 2, 3, Examples 1,2 ).
•
Know how to find the angle between two vectors (WeBWorK 3, 6, 8, Example 3).
•
Know how to determine whether two vectors are orthogonal, parallel or neither (WeBWorK 3, 4, 5, hw #20, Example 4)
•
Know how to find scalar and vector projections of a vector in the direction of another vector. (WeBWorK 7, 9, Example