Answer:
r(t) = 8(1 - t)i + 6j + (8 - t)k
Step-by-step explanation:
Given the points P(8, 6, 8) and Q(0, 6, 7), we want to find r(t).
First, find the velocity function v(t).
v(t) = <(0 - 8), (6 - 6), (7 - 8)>
= <-8, 0, -1>
Let a = -8, b = 0, and c = -1.
Where a, b, and c are the direction numbers.
Let us choose the point P(8, 6, 8), as we need an initial point on the line.
x_0 = 8
y_0 = 6
z_0 = 8
Note that
x = x_0 + at
y = y_0 + bt
z = z_0 + ct
Next, we form a parametric equation
x = 8 - 8t
y = 6 + 0t = 6
z = 8 - t
Finally,
r(t) = x(t)i + y(t)j + z(t)k
= 8(1 - t)i + 6j + (8 - t)k
