TS EAMCET 6-Aug-2021 Shift 2 Question Paper

Equation of plane passing through (2,−3,4) having DR′s(a,b,c) is given by
a⋅(x−2)+b(y+3)+c(z−4)=0
∴⇒‌‌ax+by+cz−2a+3b−4c=0‌‌...(i
Since, Eq. (i) is perpendicular to both the planes 2x−3y+5z=2 and x+y+2z=3
‌ So, ‌‌2a−3b+5c=0 . . . (ii)
‌ and ‌‌a+b+2c=0 . . . (iii)
On solving Eqs. (i) and (ii), we get
‌

a

−6−5

=‌

b

5−4

=‌

c

2+3

=k( say )
(a,b,c)=(−11k,k,5k)
From Eq. (i), we get
−11x+y+5z−2×(−11)+3×1−4×5=0
−11x+y+5z=−5
⇒‌‌x−‌

1

11

y−‌

5

11

z=‌

5

11

On comparing with x+py+qz=r,r=5∕11