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Question

Mathematics Question on introduction to three dimensional geometry

A point on XOZXOZ plane divides the join of (5,−3,−2)(5,-3,-2) and (1,2,−2) (1,2,-2) on

A

(135,0,−2)(\frac{13}{5},0,-2)

B

(135,0,2)(\frac{13}{5},0,2)

C

(5, 0, 2)

D

(5, 0, - 2)

Answer

(135,0,−2)(\frac{13}{5},0,-2)

Explanation

Solution

Let xzxz-plane i.e., yi.e., \,y = 0 divide join of (5,−3,−2)(5, -3,-2) and (1, 2, - 2) in the ratio K : 1 at the point P(x,y,z)(x, y, z)
∴\therefore x=K+5K+1,y=2K−3K+1,z=−2K−2K+1x = \frac{K+5}{K+1} , y = \frac{2K-3}{K+1}, z = \frac{-2K-2}{K+1}
Since this P lies on yy = 0 ∴\therefore = 2K−3K+1\frac{2K - 3}{K+1} = 0
∴\therefore K = 32\frac{3}{2}
∴\therefore P = (32+532+1,   0,  −2(32)−232+1)\left(\frac{\frac{3}{2}+5}{\frac{3}{2}+1}, \,\,\, 0, \,\, \frac{-2\left(\frac{3}{2}\right)-2}{\frac{3}{2}+1}\right)
i.e., (135,0,−2)i.e., \, \left( \frac{13}{5} , 0 ,- 2 \right)