Army Group X Practice Set 4

The equation of a plane which passesthrough the point (3,2,0) is
A(x−3)+B(y−2)+C(z−0)=0....(i)
where A,B,C are the direction ratios of the plane.
Given line,

x−3

1

=

y−6

5

=

z−4

4

Any point on this line (3,6,4) anddirection ratios of this line 1, 5, 4i.e a=1,b=5,c=4
Plane (i) passes through this line.
∴Point(3,6,4) lies on the plane.
A(3−3)+B(6−2)+C(4−0)=0
⇒OA+4B+4C=0
⇒B+C=0.....(ii)
and Aa+Bb+Cc=0
⇒A+5B+4C=0.....(iii)
Solving Eqs. (ii) and ( iii), A=C,B=−C
Putting these value in Eq. (i), equation ofplane is x−y+z−1=0.