KEAM 2019 Math Paper

Equation of horizontal plane through origin
2x−3y+z=0
The direction ratios of the line of intersection of the planes
2x−3y+z=0 and 3x−2y+z=5 are given
by ‌‌2a−3b+c=0
and 3a−2b+c=0
∴ ‌

a

−1

=‌

b

1

=‌

c

5

Let l,m,n be the DC's of the line of greatest slope, because the line of greatest slope is perpendicular to the line of intersection of the given plane with the horizontal plane.
−l+m+5n=0
and 3l−2m+n=0
So, ‌

l

11

=‌

m

16

=‌

n

−1

∴DC′s are proportional to (11,16,−1)