Sec1ExamReview

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Review:
1.) vectors, dot product
dot product of two vectors is done by summing their components. Geometrically it is the length of A
multiplied by the length of B multiplied by the cosine of the angle between them.
Applications include finding angles and testing for perpendicularity
Practice 1A: Practice exam problem 1.

2.) Cross-product (with determinants):
<math>\begin{vmatrix}i\ \ j\ \ k \\ a1\ b1\ c1 \\ a2\ b2\ c2\end{vmatrix}\mathrm{\ =\ A\ x\ B}</math>

Applications include triangle area = 1/2 |A x B|.
Finding normal vectors, equation of a plane ax+by+cz = d generates normal vector <a,b,c>=N
Practice test problem 5 includes normal finding

equations of lines, find where line intersects a plane
P(t) moving on line with velocity v
<math>\mathrm{P(t) = P_0 + t*}\vec{v}</math>
taylor series is not on the exam

3.) Matricies, linear systems, inverting matricies
AX=B
if <math>\mathrm{det(A)\ <>\ 0\ then\ X\ =\ A^{-1}\ .\ B}</math>
if det(A) = 0 then there are no solutions or infinitely many solutions
rotating matrices is not on the test, can be useful info outside of the class in the future though

4) Finding parametric equations
Could be similar to ones on practice exam
Equations r = r(t), velocity, acceleration. Differentiating vector identities
Kelper's law not needed to know for exam
Examples are in practice test problems 2,4,6
Applications include Cycloid, sphere properties, xy-equations

"solve by using vector methods" includes systems of equations, etc. instead of other methods

<math>\mathrm{Unit\ tension\ vector\ =\ T\ =\ }\vec{v}\mathrm{\ /\ |}\vec{v}\mathrm{|}</math>

how to take derivative of dot or cross product is needed to be known for exam (e.g. product rule)

need to be able to know how to find a component of a vector in a certain direction