Question

(a) Find a parametric equation for the line through the point (5,4,4) and in the direction of ai +bj +ck . (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.

Name: a find a parametric equation for the line through the point 544 and in the direction of ai bj ck b find conditions on abc so that the line you found in part a goes through the origin be sure 49356
Uploaded: 2022-09-22T20:51:41-08:00
Duration: 2 min 46 s
Channel: Frank Deng
Description: a find a parametric equation for the line through the point 544 and in the direction of ai bj ck b find conditions on abc so that the line you found in part a goes through the origin be sure 49356

          (a) Find a parametric equation for the line through the point (5,4,4) and in the direction of ai +bj +ck . 
(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.

Added by Elizabeth O.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Frank Deng

09/22/2022

Step 1

**Step 2:** To find conditions on a, b, c so that the line passes through the origin (0,0,0), we set x = y = z = 0 in the parametric equations: 0 = 5 + at 0 = 4 + bt 0 = 4 + ct Solving these equations simultaneously, we get: a = -5/t b = -4/t c = -4/t **Step Show more…

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(a) Find a parametric equation for the line through the point (5,4,4) and in the direction of ai +bj +ck . (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.