Homework 2, Math 152-205, additional problem:

(Part a)
Consider the following operations on two vectors  a = [ a1 a2 ]  and  
b = [ b1 b2 ]  in the plane (i.e., 2-dimensional space):

(1) The dot product of  a  and  b
(2) The cosine of the angle from  a  to  b  , assuming 
(3) The sine of the angle from  a  to  b
(4) The determinant of the matrix

[ a1  a2 ]
[        ]
[ b1  b2 ]

Which of these operations remain the same when you switch  a  and  b  , 
and which of these operations changes sign?

Consider the operation on two vectors,  a = [ a1 a2 a3 ] and
b = [ b1 b2 b3 ] in 3-space:

(5) The cross product of  a  and  b .

Does this operation remain the same when you switch  a  and  b  , or does
it change sign?

(Part b)

Answer the following question in a few sentences:

Which of the operations (1)-(5) occur together in the Froese-Wetton notes (just
look at the table of contents...)? Why should some of these operations be
discussed together?  How does this relate to your answer in (Part a)?