Concept:For two lines to be parallel, their direction ratios must be proportional.
Explanation:The first line joins
(2,1,4) and
(a−1,4,−1).
Its direction ratios are:
(a−1−2,4−1,−1−4)=(a−3,3,−5)The second line joins
(0,2,b−1) and
(5,3,−2).
Its direction ratios are:
(5−0,3−2,−2−(b−1))=(5,1,−b−1)Since the lines are parallel, the ratios are proportional:
(a−3,3,−5)=k(5,1,−b−1)Comparing the second component gives
3=k(1), so
k=3.
Using the first component:
a−3=3×5a−3=15a=18Using the third component:
−5=3(−b−1)−5=−3b−3−2=−3bb=32​Thus,
b and
a are
32​ and
18 respectively.
Answer:32​,18Hence, the correct option is
Option C.