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EAMCET Engineering 2003 Solved Paper

Section: Mathematics

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Question : 101 of 160

Marks: +1, -0

\text{XOZ}

-plane divides the join of

(2,3,1)

(6,7,1)

$3:7$
$2:7$
$-3:7$
$-2:7$

Solution:

Let

\text{X O Z}

-plane divides the joining the point

(2,3,1)

and

(6,7,1)

into

m:n

, then the co-ordinate of

\text{X O Z}

-plane is

\left(\; \frac{m x_2+n x_1}{m+n},\; \frac{m y_2+n y_1}{m+n},\; \frac{m z_2+n z_1}{m+n} \;\right)

= \left(\; \frac{6 m+2 n}{m+n},\; \frac{7 m+3 n}{m+n},\; \frac{m+n}{m+n} \;\right)

But on the XOZ-plane

y

-coordinate will be zero, then

\;\; \frac{7 m+3 n}{m+n}=0 \Rightarrow\; \frac{m}{n}=-\frac{3}{7}

\therefore \;\; m:n=-3:7

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