pg. 716, #11 (moderate)

Show that the line through the points (2,-1,-5) and (8,8,7) is parallel to the line through

the points (4,2,-6) and (8,8,2).

Solution:

The vector from (2,1,-5) to (8,8,7) has direction <8-2, 8-(-1),7 -(-5) > = <6,9,12> = 6<1,3/2,2>.

The vector from (4,2,-6) to (8,8,2) has direction <4,6,8> = 4<1,3/2,2>. Both are parallel to <1,3/2,2>