1.
The dot product is a ________ while the cross product is a _________
2.
Two vectors whose dot product is 0 are ____________, two vectors whose cross
product is 0 are __________
3.
Find the volume of the parallelepiped determined by
i
+ 2
j
– 3
k
, 2
i
–
j
+ 2
k
, 
i
–
j
+3
k
4.
Find parametric equations for the line through the point (0,1,2) that is parallel to the
plane 2x  y + 3z = 4 and perpendicular to the line x = 2 + t, y = 1 – t, z = 3 +2t
5.
Find the distance between the given parallel planes 4x + 8y – 10z = 6,
2x + 4y – 5z = 1
6.
Find an equation for the plane that passes through the line of intersection of the planes
x  2z = 1 and y – z = 3 and is perpendicular to the plane x – y + 2z = 2
7.
Are the lines defined by the following equations parallel, intersecting or skew?
L1: x = t, y = 1+2t, z=2+3t
L2: x=34s, y=23s, z=1+2s
8.
A curve has the given vector equation:
r
(t) = <1, 2cos(t), sin(t)>
a)
Write parametric equations for the curve
b)
Sketch the curve
9.
Two particles are traveling on different paths given by
r
1
(t) = <t, t + 1, t
2
+ 1> and
r
2
(s)
= <8s – 5, s + 3, 10s >
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 Spring '09
 Penner
 Dot Product, Parametric equation

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