UPSC NDA Math Model Paper 9

Let, direction ratios of line be < a, b, c >
If line is parallel to plane means, Normal of plane and line will be perpendicular
∴a1a2+b1b2+c1c2=0
Direction ratios of line be < a, b, c >
Given: Line is parallel to the plane x + y + z = 1 and 2x – y - 2z = 3.
Direction ratios of plane x + y + z = 1 are < 1, 1, 1 >
a + b + c = 0 …. (1)
Direction ratios of plane 2x – y - 2z = 3 are < 2, -1, -2 >
2a – b – 2c = 0 …. (2)
Solve, (1) and (2),

a

−2+1

=−

b

−2−2

=

c

−1−2

⇒

a

−1

=

b

4

=c−3 OR

a

1

=

b

−4

=

c

3

‌
∴ Direction ratios < 1, - 4, 3 >
Hence, option (3) is correct