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Stewart_Calc_7ET ch12sec01
MULTIPLE CHOICE
1. Suppose you start at the origin, move along the x-axis a distance of units in the positive
direction, and then move downward a distance of units. What are the coordinates of your
position?
a.
b.
c.
d.
e.
2. Find that the midpoint of the line segment from to .
a.
b.
c.
d.
e.
3. Find the center and radius of the sphere.
a.
b.
c.
d.
e.
none of these
4. Plot the given points in a three-dimensional coordinate system.
(1, 2, 3)
a.
c.
b.
d.
5. Find the length of each side of the triangle ABC and determine whether the triangle is an isosceles
triangle, a right triangle, both, or neither.
A (–1, 0, 1), B (1, 1, –1), C (1, 1, 1)
a.
1, 1, , both
b.
1, 2, , neither
c.
3, 2, , right
d.
1, 1, , isosceles
6. Find the standard equation of the sphere with center C and radius r.
C (3, –5, 3); r = 7
a.
(x – 3)2 + (y + 5)2 + (z – 3)2 = 7
b.
(x – 3)2 + (y + 5)2 + (z – 3)2 = 49
c.
(x + 3)2 + (y – 5)2 + (z + 3)2 = 49
d.
(x + 3)2 + (y – 5)2 + (z + 3)2 = 7
7. Find the distance from to the xy-planes.
a.
8
b.
16
c.
10
d.
2
e.
4
8. Find an equation of the sphere with center that touches the xy-plane.
a.
b.
c.
d.
e.
9. Sketch the plane in a three-dimensional space represented by the equation.
z = 2
a.
c.
b.
d.
10. Determine whether the given points are collinear.
A (–3, –2, –3), B (–9, –5, 0), and C (–1, –1, –4)
a.
Not collinear
b.
Collinear
11. Find the midpoint of the line segment joining the given points.
(–5, 0, 2) and (–3, –2, 4)
a.
( , , )
c.
( , , )
b.
( , , )
d.
( , , )
12. Find the center and the radius of the sphere that has the given equation.
+ + – 6x + 4y = 0
a.
( –3, 2, 0),
c.
( –3, 2, 0), 13
b.
( 3, –2, 0), 13
d.
( 3, –2, 0),
NUMERIC RESPONSE
1. a. Find an equation of the sphere that passes through the point and has center
.
b. Find the curve in which this sphere intersects the xy-plane.
−1
−1
−1
−1
1
−1
−1
1
3
−4
−1
3
13
13
2. Write an inequality to describe the half-space consisting of all points to the left of a plane
parallel to the xz-plane and units to the right of it.
3. Write inequalities to describe the solid rectangular box in the first octant bounded by the
planes , , and .
4. Write an inequality to describe the region consisting of all points between (but not on) the
spheres of radius and centered at the origin.
5. Find an equation of the sphere that passes through the point and has center
.
6. Draw a rectangular box with the origin and as opposite vertices and with its faces
parallel to the coordinate planes. Find the length of the diagonal of the box.
7. Write inequalities to describe the solid upper hemisphere of the sphere of radius centered at the
origin.
8. Find the length of the median of side AB of the triangle with vertices
