Question

Determine whether any of the lines are parallel or identical.

L1: x = 3 + 2t, y = −6t, z = 1 − 2t,

L2: x = 1 + 2t, y = −1 − t, z = 3t,

L3: x = −1 + 2t, y = 3 − 10t, z = 1 − 4t,

L4: x = 5 + 2t, y = 1 − t, z = 8 + 3t.

Answer 1

L2 and L3 are parallel

On differentiating equation in L2 we get:

$\frac{\delta x}{\delta t}=2$ , $\frac{\delta y}{\delta t}=-1$ ,$\frac{\delta z}{\delta t}=3$

On differentiating equation in L3 we get:

$\frac{\delta x}{\delta t}=2\ \ \\ \frac{\delta y}{\delta t}=-1\ \\ \ \frac{\delta z}{\delta t}=3$

hence equations in L2 and L3 are parallel