MHT CET 2021 Math Solved Paper

Given equation of line
‌

x−2

3

=‌

y−1

−5

=‌

z+2

2

. . . (i)
The direction ratios of the normal are (1,3,−α).
The direction ratios of the line are (3,−5,2) and equation of given plane
x+3y−az+β=0 . . . (ii)
Four lines are perpendicular
⇒‌a1a2+b1b2+c1c2=0
⇒‌3−15+2α=0
⇒‌2α=−12⇒α=−6
(2,1,−2) lies on the plane, so
2+3+6(−2)+β‌‌=0⇒β=7
α⋅β‌‌=−6×7=−42