Do the lines intersect? $l _ { 1 } : x = - 5 t + 1 , y = - 7 t + 1 , z = 3 t$ $l _ { 2 } : x = 12 t + 3 , y = 7 , z = - 11 t - 6$

Name: Do the lines intersect? $l _ { 1 } : x = - 5 t + 1 , y = - 7 t + 1 , z = 3 t$ $l _ { 2 } : x = 12 t + 3 , y = 7 , z = - 11 t - 6$
Brand: Quizplus
Rating: 4.8 (32 reviews)

Question

Quizplus · Accepted Answer

The lines do not intersect because they lie in parallel planes. The first line's y-coordinate changes with $t$, while the second line's y-coordinate is constant, indicating they cannot intersect.

Do the Lines Intersect l1:x=−5t+1,y=−7t+1,z=3tl _ { 1 } : x = - 5 t + 1 , y = - 7 t + 1 , z = 3 tl1​:x=−5t+1,y=−7t+1,z=3t

Do the Lines Intersect $l _ { 1 } : x = - 5 t + 1 , y = - 7 t + 1 , z = 3 t$