If the line


If the line $\frac{x-2}{3}=\frac{y+1}{2}=\frac{z-1}{-1}$ intersects the palne $2 x+3 y-z+13=0$ at a point $P$ and the plane $3 x+y+4 z=16$ at a point $Q$, then PQ is equal to :

  1. $2 \sqrt{14}$

  2. $\sqrt{14}$

  3. $2 \sqrt{7}$

  4. 14

Correct Option: 1



$\mathrm{x}=3 \lambda+2, \mathrm{y}=2 \lambda-1, \mathrm{z}=-\lambda+1$

Intersection with plane $2 x+3 y-z+13=0$

$2(3 \lambda+2)+3(2 \lambda-1)-(-\lambda+1)+13=0$

$13 \lambda+13=0 \quad \lambda=-1$

$\therefore \quad P(-1,-3,2)$

Intersection with plane

$3 x+y+4 z=16$

$3(3 \lambda+2)+(2 \lambda-1)+4(-\lambda+1)=16$



$\mathrm{PQ}=\sqrt{6^{2}+4^{2}+2^{2}}=\sqrt{56}=2 \sqrt{14}$

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