Find a function
r (t )
that describes the line segment from Upper
P (8 , 6, 8 ) to Upper Q (0, 6, 7 ) (inclusively).

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

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step-by-step explanation: