(a) Find a parametric equation for the line through the point (5,4,4) and in the

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.

(1 point) (a) Find a parametric equation for the line through the point (5,4,4)land in the direction of ai bj c (b) Find conditions on a, b, clso 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 -I Choice 2: a -I

Explanation / Answer

a) r= r0 + t(ai+bj+ck)

therefore, r =xi+yj+zk = 5i+4j+4k + t(ai+bj+ck)

b) For this line to pass through origin, (0,0,0) must satisfy the equation,

Therefore, 5+ta=0 , a= -5/t

4+tb=0 , b= -4/t

4+tc= 0 , c= -4/t

Therefore, two distinct triples of a,b,c can be found by putting t= 1 and 2 respectively

we will get

Choice 1 : a=-5 , b=-4, c=-4

Choice 2 : a=-5/2, b=-2, c= -2

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