   Chapter 11.5, Problem 26E

Chapter
Section
Textbook Problem

# Determining Parallel Lines In Exercises 25-28, determine whether any of the lines are parallel or identical. L 1 : x = 3 + 2 t ,   y = − 6 t ,   z = 1 − 2 t L 2 : x = 1 + 2 t ,   y = − 1   − t ,     z = 3 t L 3 : x = − 1 + 2 t ,   y = 3 − 10 t ,   z = 1 − 4 t L 4 : x = 5 + 2 t ,   y = 1 − t ,   z = 8 + 3 t

To determine

Whether any of the four lines, L1:x=3+2t,y=6t,z=12t, L2:x=1+2t,y=1t,z=3t, L3:x=1+2t,y=310t,z=14t, and L4:x=5+2t,y=1t,z=8+3t are parallel or identical.

Explanation

Consider the four lines,

L1:x=3+2t,y=6t,z=12t,

L2:x=1+2t,y=1t,z=3t,

L3:x=1+2t,y=310t,z=14t,

And,

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

The corresponding direction vectors are,

v1=2,6,2,

v2=2,1,3,

v3=

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