UPSC NDA Math Model Paper 3

Here, Plane passing through points A (2, 2, 1), B(3, 4, 2) and C (7, 0, 6)
Equation of plane = |

x−2	y−2	z−1
3−2	4−2	2−1
7−3	0−4	6−2

|=0
⇒(x−2)(8−(−4))−(y−2)(4−4) +(z−1)(−4−8)=0
⇒12x−24−12z+12=0
⇒x−z−1=0
Now, to find point which lies on plane lets check from options
(1,0,0):x−z−1=0 ⇒1−0−1=0
This point satisfies the equation
Hence, option (1) is correct.