Find a vector parametric equation r(t) for the line through the points P = (4, -3, 4) and Q = (3, -6, 2) for each of the given conditions on the parameter t. (a) If (0) = (4, −3, 4) and (2) 3t t r(t) = <4- -,-3 (b) If 7(6) = P P r(t) =<7- - and 7(8): and - t r(t) = <4- 4' = 7(8) = Q, then 6 3,10-t> - ,4-t> (c) If the points P and Q correspond to the parameter values t = 0 and t = -4, respectively, then 3t 4 (3, -6, 2), then

Algebra and Trigonometry (MindTap Course List)
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Chapter8: Polar Coordinates And Parametric Equations
Section8.CT: Chapter Test
Problem 8CT
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Find a vector parametric equation r(t) for the line
through the points P = (4, -3, 4) and Q = (3, -6, 2)
for each of the given conditions on the parameter t.
(a) If 7 (0)
=
(4, −3, 4) and 7(2) = (3, −6, 2), then
r(t) = <4- -3
r(t) =
(b) If 7(6)=
= P
r(t) = <7-
t
2
2
P and 7(8)
and
= <4-
-
14
9
3t
2
4-t>
(c) If the points P and Q correspond to the parameter
values t = 0 and t = -4, respectively, then
=
3t
3,4->
-3
9
7(8) = Q, then
3t
121,6-321 ,10-t>
Transcribed Image Text:Find a vector parametric equation r(t) for the line through the points P = (4, -3, 4) and Q = (3, -6, 2) for each of the given conditions on the parameter t. (a) If 7 (0) = (4, −3, 4) and 7(2) = (3, −6, 2), then r(t) = <4- -3 r(t) = (b) If 7(6)= = P r(t) = <7- t 2 2 P and 7(8) and = <4- - 14 9 3t 2 4-t> (c) If the points P and Q correspond to the parameter values t = 0 and t = -4, respectively, then = 3t 3,4-> -3 9 7(8) = Q, then 3t 121,6-321 ,10-t>
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