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Introduction to Three Dimensional Geometry — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsIntroduction to Three Dimensional Geometry1 Mark
MCQ
The ratio in which $yz-$plane divides the line segment joining $(-3, 4, 2), (2, 1, 3)$ is:
  • A
    $-4 : 1$
  • ✓
    $3 : 2$
  • C
    $-2 : 3$
  • D
    $1: 4$
✓

Answer

Correct option: B.
$3 : 2$
Let the plane divide the line in the ratio $p : 1$
A point that divides the line joining these $2$ points in the ratio $p : 1$
given by $\Big(\frac{2\text{p}-3}{\text{p}+1},\frac{\text{p}+4}{\text{p}+1},\frac{3\text{p}+2}{\text{p}+1}\Big)$
Since, this point has to lie on the $zy-$plane.
so, $2p - 3 = 0$
$\Rightarrow\text{p}=\frac{3}{2}$

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