Larson_Calculus_10e ch11sec05
MULTIPLE CHOICE
1. Find a set of parametric equations of the line through the point parallel to the vector
.
a.
b.
c.
d.
e.
2. Find a set of symmetric equations of the line through the point parallel to the vector
.
a.
b.
c.
d.
e.
3. Find the set of parametric equations of the line through the point that is parallel to the line
, ,and .
a.
b.
c.
d.
e.
4. Find a set of parametric equations of the line through the points and .
a.
b.
c.
d.
e.
5. Find a set of symmetric equations of the line through the points and .
a.
b.
c.
d.
e.
6. Find a set of parametric equations of the line that passes through the point and is parallel
to the xy–plane and yz–plane.
a.
b.
c.
d.
e.
7. Determine whether any of the lines given below are parallel or identical.
a.
are identical
b.
are identical
c.
are identical
d.
are parallel
e.
are parallel
8. Determine whether any of the lines given below are parallel or identical.
a.
are parallel
b.
are identical
c.
are parallel
d.
are identical
e.
are parallel
9. Determine whether the lines given below intersect, and, if so, find the point of intersection.
a.
The lines intersect at .
b.
The lines are parallel.
c.
The lines intersect at .
d.
The lines intersect at .
e.
The lines are not parallel but do not intersect.
10. Determine whether the lines given below intersect, and, if so, find the point of intersection.
a.
The lines are parallel.
b.
The lines intersect at .
c.
The lines intersect at .
d.
The lines intersect at .
e.
The lines are not parallel but do not intersect.
11. Find an equation of a plane passing through the given point and perpendicular to the given vector.
Point: Vector:
a.
b.
c.
d.
e.
12. Find an equation of a plane passing through the following three points.
a.
b.
c.
d.
e.
13. Find an equation of a plane passing through the points
and perpendicular to the plane
.
a.
b.
c.
d.
e.
14. Determine whether the following planes are parallel, orthogonal, or neither. If they are neither parallel
nor orthogonal, find the angle of intersection.
a.
The planes are neither parallel nor orthogonal, the angle of intersection is .
b.
The planes are parallel.
c.
The planes are neither parallel nor orthogonal, the angle of intersection is .
d.
The planes are orthogonal.
15. Determine whether the following planes are parallel, orthogonal, or neither. If they are neither parallel
nor orthogonal, find the angle of intersection.
a.
The planes are neither parallel nor orthogonal, the angle of intersection is .
b.
The planes are neither parallel nor orthogonal, the angle of intersection is .
c.
The planes are orthogonal.
d.
The planes are parallel.
16. Find the distance between the point and the plane .
a.
b.
c.
d.
e.
17. Find the distance between the planes given below.
a.
b.
c.
d.
e.
18. Find the distance between the point and the line given by the set of parametric equations
.
a.
/11
b.
2
c.
/11
d.
4
e.
1
5 22
3 110
19. A chute at the top of a grain elevator of a combine funnels the grain into a bin (see figure). Find the
angle between two adjacent sides. Round your answer to one decimal place.
a.
b.
c.
d.
e.
20. Two insects are crawling along different lines in three-space. At time t (in minutes), the first insect is
at the point where . Also, at time t, the second insect is at the
point where . Assume distances are given in inches. Find the distance
between the two insects at time . Round your answer to two decimal places.
a.
inches
b.
inches
c.
inches
d.
inches
e.
inches
21. Two insects are crawling along different lines in three-space. At time t (in minutes), the first insect is
at the point where . Also, at time t, the second insect is at the point
where . Assume distances are given in inches. How close do the
insects get? Round your answer to two decimal places.
a.
inches
b.
inches
c.
inches
d.
inches
e.
inches