Math, asked by nehemiya123456789, 11 months ago

26.
Find the coordinates of the point where the line through (-1, 1, - 8) and
(5,-2, 10) crosses the ZX plane.​

Answers

Answered by ColinJacobus
5

\fontsize{18}{10}{\textup{\textbf{The co-ordinates of the point are (-3, 0, 6).}}}

Step-by-step explanation:

Let m : n be the ratio in which the line joining the points (-1, 1, -8) and (5, -2, 10) is divided by the ZX plane at a point P (let).

Then, the co-ordinates of the point P are given by

\left(\dfrac{m\times5+n\times(-1)}{m+n},\dfrac{m\times(-2)+n\times1}{m+n},\dfrac{m\times10+n\times(-8)}{m+n}\right)\\\\\\=\left(\dfrac{5m-n}{m+n},\dfrac{-2m+n}{m+n},\dfrac{10m-8n}{m+n}\right).  

Since the point P lies on the ZX plane, so its y co-ordinate will be zero.

That is, we must have

\dfrac{-2m+n}{m+n}=0\\\\\Rightarrow -2m+n=0\\\\\Rightarrow 2m=n\\\\\Rightarrow \dfrac{m}{n}=\dfrac{1}{2}.

Therefore, the x and z co-ordinates of P are

x=\dfrac{5m-n}{m+n}=\dfrac{5\frac{m}{n}-1}{\frac{m}{n}+1}=\dfrac{5\times\frac{1}{2}-1}{\frac{1}{2}-1}=\dfrac{5-2}{1-2}=-3,\\\\\\z=\dfrac{10m-8n}{m+n}=\dfrac{10\frac{m}{n}-8}{\frac{m}{n}+1}=\dfrac{10\times\frac{1}{2}-8}{\frac{1}{2}-1}=\dfrac{10-16}{1-2}=6.

Thus, the required co-ordinates of the point are (-3, 0, 6).

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