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UPSC NDA I 2026 Mathematics Paper

Question Numbers: 55-56

For the next two (02) items that follow:

A line L passing through the point

(-1,2,-3)

is perpendicular to the plane

P

given by

2 x+3 y+z+5=0

Question : 56 of 120

Marks: +1, -0

What are the direction ratios of a line M parallel to the plane P ?

Solution:

Concept:

A line parallel to a plane is perpendicular to the plane’s normal vector.

Explanation:

Plane

P

2x+3y+z+5=0

, so its normal vector is

\langle 2,3,1 \rangle

Direction ratios

\langle a,b,c \rangle

of a line parallel to

P

must satisfy:

2a+3b+c=0.

Check option D:

\langle 2,2,-10 \rangle

2(2)+3(2)+1(-10)=4+6-10=0.

Thus option D is correct.

Answer:

\langle 2,2,-10 \rangle

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