3D Geometry 2 Question 4

####4. If the line, $\frac{x-3}{2}=\frac{y+2}{-1}=\frac{z+4}{3}$ lies in the plane, $l x+m y-z=9$, then $l^{2}+m^{2}$ 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 $\frac{x-3}{2}=\frac{y+2}{-1}=\frac{z+4}{3}$ lies in the plane $l x+m y-z=9$, therefore we have $2 l-m-3=0$

$[\because$ normal will be perpendicular to the line] $\Rightarrow \quad 2 l-m=3$ …..(i)

and

$ 3 l-2 m+4=9 $

$ [\because \text { point }(3,-2,-4) \text { lies on the plane }] $

$ 3 l-2 m=5 …..(ii) $

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

$ \begin{gathered} l=1 \text { and } m=-1 \\ l^{2}+m^{2}=2 \end{gathered} $



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