Are the lines parallel? $l _ { 1 } : x = 2 t + 5 , y = 3 t + 3 , z = - 4 t - 2$ $l _ { 2 } : x = 5 t + 1 , y = 2 t - 4 , z = 11 t + 7$

Question

Quizplus · Accepted Answer

The direction vectors of the lines $l_1$ and $l_2$ are not proportional. For $l_1$, the direction vector is $<2, 3, -4>$, and for $l_2$, it is $<5, 2, 11>$. Since these vectors are not scalar multiples of each other, the lines are not parallel.

Are the Lines Parallel l1:x=2t+5,y=3t+3,z=−4t−2l _ { 1 } : x = 2 t + 5 , y = 3 t + 3 , z = - 4 t - 2l1​:x=2t+5,y=3t+3,z=−4t−2

Are the Lines Parallel $l _ { 1 } : x = 2 t + 5 , y = 3 t + 3 , z = - 4 t - 2$