Math 251, Spring 2008, Quiz 1 Solutions
Describe the region defined by
x
=
y
=
z
. How about
x
=
y
=
z
2
?
What if you had just
x
=
z
2
. Draw a picture in all three cases to get
full credit. This part is worth 6 marks.
We did in recitation last time that
vector
b

proj
vectora
vector
b
is orthogonal to
vectora
because projection of a vector
vector
b
onto
vectora
gives us the component of
vector
b
in
the direction of
vectora
. We’ll try an analogue of that for cross products.
Let
vectora,
vector
b
be two given vectors. Consider
pp
vectora,
vector
b
vector
c
=
vector
c

(
vector
c.
vectora
×
vector
b

vectora
×
vector
b

)
vectora
×
vector
b

vectora
×
vector
b

.
What kind of a vector is this? Draw a picture and describe your
answer in words. You neednt prove anything here. This part is worth
4 marks.
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 Spring '08
 Beck
 Math, Dot Product

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