Write the ratio in which YZ-plane divides the segment joining P(-… - Vidyadip

Question

Write the ratio in which YZ-plane divides the segment joining P(-2, 5, 9) and Q(3, -2, 4).

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Answer

Let the YZ-plane divides the line segment joining points P(-2, 5, 9) and Q(3, -2, 4) in the ratio k : 1.
Using the setion formula, the coordinates of the point of intersection are given by
$\Big(\frac{\text{k}(3)-2}{\text{k}+1},\frac{\text{k}(-2)+5}{\text{k}+1},\frac{\text{k}(4)+9}{\text{k}+1}\Big)$
On the YZ-plane, the X-coordinate of any point is zero.
$\frac{\text{k}(3)-2}{\text{k}+1}=0$
Implies that 3k - 2 = 0
Implies that $\text{k}=\frac{2}{3}$
Thus, the YZ-plane divides the line segment formed by joining the given points in the ratio 2 : 3 internally.

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