AP EAPCET 23-Aug-2021 Shift 1 Paper

Let image of point A across x+y+z=12 be s(p,q,r) Then, equation of line will be

p−1

1

=

q−2

1

=

r−3

1

=

−2(1+2+3−12)

12+12+12

=

12

3

=4
∴

p−1

1

=4⇒p=5

q−2

1

=4⇒q=6

1−3

1

=4⇒r=7
∴S(p,q,r)=S(5,6,7)
Now, equation of line CS will be

x−5

5−3

=

y−6

6−5

=

z−7

7−9

x−5

−2

=

y−6

−1

=

z−7

2

=λ (say)
∴x=−2λ+5,y=6−λ,z=2λ+7
Thus, coordinate of B will be ((−2λ+5),(6−λ),(2λ+7))
Since, B lies on given plane.∴(−2λ+5)+(6−λ)+(2λ+7)=12
⇒λ=6
∴B=(−7,0,9)
∴OB=√(−7−0)2+(0−0)2+(19−0)2 =√410