3D Geometry 2 Question 4

####4. If the line, x32=y+21=z+43 lies in the plane, lx+myz=9, then l2+m2 is equal to

(2016 Main)

(a) 26

(b) 18

(c) 5

(d) 2

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Answer:

Correct Answer: 4. (d)

Solution:

  1. Since, the line x32=y+21=z+43 lies in the plane lx+myz=9, therefore we have 2lm3=0

[ normal will be perpendicular to the line] 2lm=3 …..(i)

and

3l2m+4=9

[ point (3,2,4) lies on the plane ]

3l2m=5..(ii)

On solving Eqs. (i) and (ii), we get

l=1 and m=1l2+m2=2



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