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Math E-21a – Midterm Exam 1 Topics – Fall 2009
1. Given vectors in
R
2
or
R
3
, do addition, scalar multiplication, dot and cross products, scalar and vector projection.
2. Manipulate vector expressions symbolically (distributive law, triple product,
A
(
B
C
), etc.).
3. Express lengths, angles, areas of triangles and parallelograms, and volumes of parallelepipeds and tetrahedra in
terms of vectors. Identify and construct orthogonal (perpendicular) vectors.
4. Given sufficient data, describe a line or plane either parametrically or in terms of one or more equations
involving
x
,
y
, and
z
.
5. Calculate the intersection (if any) of specified lines and planes. Resolve a vector into components parallel and
perpendicular to a specified vector, line, or plane.
6. Calculate the distance from a point to a specified line or plane, or between two nonintersecting lines in
R
3
.
7. For motion in
R
2
or
R
3
specified parametrically in terms of time, calculate and sketch position, velocity, and
acceleration vectors, and find an expression for the tangent line to the path at a specified point and for the unit
tangent vector.
8. Write one or more parameterized expressions for a specified path in
R
2
or
R
3
.
9. Develop an expression for the length of a parameterized path as an integral.
10. Sketch a graph of a parameterized path, and eliminate the parameter (if possible) to find an equation or equations in
terms of
x
,
y
, (and
z
) for the path.

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