Question

(a) Find a parametric equation for the line through the point (5, 2, 3) and in the direction of ai + bj + ck. r(t) = (b) Find conditions on a, b, c so that the line you found in part (a) goes through the origin. (Be sure you can give a reason for your answer.) Then use your work to give two distinct triples a, b, c that result in the line passing through the origin. Choice 1: a = , b = , c = ; Choice 2: a = , b = , c = .

          (a) Find a parametric equation for the line through the point (5, 2, 3) and in the direction of ai + bj + ck.
r(t) =
(b) Find conditions on a, b, c so that the line you found in part (a) goes through the origin. (Be sure you can give a reason for your answer.) Then use your work to give two distinct triples a, b, c that result in the line passing through the origin.
Choice 1: a = , b = , c = ;
Choice 2: a = , b = , c = .

(a) Find a parametric equation for the line through the point (5, 2, 3) and in the direction of ai + bj + ck.
r(t) =
(b) Find conditions on a, b, c so that the line you found in part (a) goes through the origin. (Be sure you can give a reason for your answer.) Then use your work to give two distinct triples a, b, c that result in the line passing through the origin.
Choice 1: a = , b = , c = ;
Choice 2: a = , b = , c = .

Added by Josefa A.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Vincenzo Zaccaro

04/15/2022

Step 1

Step 1: The parametric equation for the line through the point (5,2,3) and in the direction of ai bj + ck is given by: \[ \textbf{r}(t) = (5,2,3) + t(a,b,c) \] Show more…

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(a) Find a parametric equation for the line through the point (5, 2, 3) and in the direction of ai + bj + ck. r(t) = (b) Find conditions on a, b, c so that the line you found in part (a) goes through the origin. (Be sure you can give a reason for your answer.) Then use your work to give two distinct triples a, b, c that result in the line passing through the origin. Choice 1: a = , b = , c = ; Choice 2: a = , b = , c = .