MHTCET 13 May 2023 Shift 2 Solved Paper

Let the equation of the plane through (2,2,2) be
a(x−2)+b(y−2)+c(z−2)=0
Since, it is parallel to the straight lines having Dr's (1,0,−1) and (−1,1,0), therefore a−c=0 and −a+b=0
⇒‌‌a=b=c
Therefore, equation of plane is
‌x−2+y−2+z−2=0
‌x+y+z=6⇒‌

x

6

+‌

y

6

+‌

z

6

=1
Its intercepts on coordinate axes are A(6,0,0),B(0,6,0) and C(0,0,6).
Hence, the volume of tetrahedron OABC
‌=‌

1

6

[abc]=‌

1

6

[

6	0	0
0	6	0
0	0	6

]
‌=‌

1

6

×6×36=36‌ cube units ‌