First slide

Introduction to 3-D Geometry

Question

Find the ratio in which the yz-plane divides the line segment formed by joining the points (- 2, 4,7) and (3, - 5, 8).

Easy

A

externally 2:3
B

internally 2:3
C

internally 3 :2
D

externally 3: 2

Solution

The given points are A(-2,4,7 ) and B(3,- 5, 8). Let the point P (0, y, z) in yz-plane divides AB in the ratio k:1, then
r-coordinate of point $P = \frac{{mx}_{2} + {nx}_{1}}{m + n}$
$\frac{k \times 3 + 1 \times (- 2)}{k + 1} = 0 [∵ x - coordinate of p is zero]$
$\begin{array}{lrl} \Rightarrow 3 k - 2 = 0 \Rightarrow k = \frac{2}{3} \\ \Rightarrow k : 1 = 2 : 3 \end{array}$
yz-plane divides the segment internally in the ratio 2:3.

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