Question

Find the ratio in which the yz-plane divides the join of the points $(-2,4,7)$ and $(3,-5,8)$ and also find the co-ordinates of the point of intersection of this line with the $yz$ - plane.

• A. $\lambda =\frac{2}{3}$ and $(0,\frac{2}{5},\frac{37}{5})$
• B. $\lambda =\frac{1}{3}$ and $(\frac{-3}{4},\frac{7}{4},\frac{29}{4})$
• C. $\lambda =\frac{2}{3}$ and $(\frac{-3}{4},\frac{7}{4},\frac{29}{4})$
• D. $\lambda =\frac{1}{3}$ and $(0,\frac{2}{5},\frac{37}{5})$

Answer 1

The correct option is A $\lambda =\frac{2}{3}$ and $(0,\frac{2}{5},\frac{37}{5})$

Let $\lambda$ be the ratio in which yz-plane divides the line joining the points $(-2,4,7)$ and $(3,-5,8)$

The co-ordinates of any point on the line joining the two points are
$(\frac{3\lambda -2}{\lambda +1},\frac{-5\lambda +4}{\lambda +1},\frac{8\lambda +7}{\lambda +1})$
If the point is in the $yz$ - plane, then its $x$-coordinate should be zero.
$\therefore \frac{3\lambda -2}{\lambda +1}=0$ or $3\lambda -2=0$

$\therefore \lambda =\frac{2}{3}.$
Hence, the required ratio is $2:3$ and putting $\lambda =\frac{2}{3}$, the required point is $(0,\frac{2}{5},\frac{37}{5}).$