AP EAMCET Engineering 2013 Solved Paper

Direction ratios of AB and AC are <1,−1,−1> and<2,−1,1>, respectively.
∴

x2−x1=1

y2−y1=−1

z2−z1=−1

} ........(i)
and

x1−x3=2

y1−y3=−1

z1−z3=1

} ........(ii)
From Eqs. (i) and (ii)
Let <a,b,c> be the direction ratio of the normal to the plane ABC.
Then, a−b−c=0
and 2a−b+c=0
By cross-multiplication method,

a

−1−1

=b−2−1=

c

−1+2

a

−2

=

b

−3

=

c

1

⇒

a

2

=

b

3

=

c

−1

So, the direction ratio of the normal to the plane ABC is <2,3,−1>