The xy-plane divided the line joining the point (-1, 3, 4) and (2… - Vidyadip

MCQ

The $xy-$plane divided the line joining the point $(-1, 3, 4)$ and $(2, -5, 6)$

A
Internally in the ratio $2 : 3$
✓
Externally in the ratio $2 : 3$
C
Internally in the ratio $3 : 2$
D
Externally in the ratio $3 : 2$

✓

Answer

Correct option: B.

Externally in the ratio $2 : 3$

Let the $XY-$plane divide the line segment joining points
$P(-1, 3, 4)$ and $Q(2, -5, 6)$ in the ratio $k : 1.$
Using the section formula, the coordinates of the point of intersection are given by
$\Big(\frac{\text{k}(2)-1}{\text{k}+1},\frac{\text{k}(-5)+3}{\text{k}+1},\frac{\text{k}(6)+4}{\text{k}+1}\Big) $
On the $XY-$plane, the $Z-$coordinate of any point is zero.
$\Rightarrow\frac{\text{k}(6)+4}{\text{k}+1}=0$
$\Rightarrow6\text{k}+4=0$
$\Rightarrow\text{k}=\frac{-2}{3}$
Thus, the $XY-$plane divides the line segment joining the given points in the ratio $2 : 3$ externally.

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