March 13, 2008
Name_________________________
Quiz 1
1. Find an equation of the sphere that passes through the origin and whose center is
(1, 1, 3).
radius = 1 + 1+ 9 = 11
Sphere has equation: (x - 1)2 + (y - 1)2 + (z - 3)2 = 11
2. If a = 3i - 2 k and b = i - j + k, find the following:
(a) 3a + 4b = 13i - 4j - 2k
(b) | b |
| b | = 1 + 1+ 1 = 3
(c) A unit vector in the direction of a
| a | = 13
u=
< 3,0,−2 >
3
−2
=<
,0,
>
13
13
13
3. If a child pulls a sled through the snow with a force of 50 N exerted at an angle of 38
degrees above the horizontal, find the horizontal and vertical components of the force.
o
Horizontal component = 50 cos(38 ) N ≈ 39.40 N
o
Vertical component = 50 sin(38 ) N ≈ 30.78 N