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Exercise 8.3
PART A
1. State the coordinates of a point on each of the given lines.
a. r ! 13, 1, 82 s11, 1, 92, sR
b.
c.
d.
e.
f.
x 1
y 1 z 3
2 1 1
x 2 3t, y 1 14t2, z 3 t, tR
x 2
1 z 1
2 , y 3
x 3, y 2, z 1 2k, kR
x 1 3
1
2
y 3 4
1
4
z 2 5
1
2
2. State a direction vector for each line in question 1, making certain that the
components for each are integers.
K
PART B
3. A line passes through the points A11, 2, 42 and B13, 3, 52.
a. Write two vector equations for this line.
b. Write the two sets of parametric equations associated with the vector
equations you wrote in part a.
4. A line passes through the points A11, 5, 42 and B12, 5, 42.
a. Write a vector equation for the line containing these points.
b. Write parametric equations corresponding to the vector equation you wrote
in part a.
c. Explain why there are no symmetric equations for this line.
5. State where possible vector, parametric, and symmetric equations for each of
the following lines.
a. the line passing through the point P11, 2, 12 with direction vector
13, 2, 12
b. the line passing through the points A11, 1, 02 and B11, 2, 12
c. the line passing through the point B12, 3, 02 and parallel to the line passing
through the points M12, 2, 12 and N12, 4, 72
d. the line passing through the points D11, 0, 02 and E11, 1, 02
e. the line passing through the points X14, 3, 02 and O10, 0, 02
f. the line passing through the point Q11, 2, 42 and parallel to the z-axis
NEL
CHAPTER 8 449