Question

find the ratio in which the line segment joining the points (-2, 4,7) and (3, -5, 8) divided by yz plane​

Answer 1

$\textbf{Given:}$

$\textsf{Points are A(-2,4,7) and B(3,-5,8)}$

$\textbf{To find:}$

$\textsf{Point of intersection of line segment joining A and B with yz plane}$

$\textbf{Solution:}$

$\textsf{The equation of line joining A and B is}$

$\mathsf{\dfrac{x-x_1}{x_2-x_1}=\dfrac{y-y_1}{y_2-y_1}=\dfrac{z-z_1}{z_2-z_1}}$

$\mathsf{\dfrac{x+2}{3+2}=\dfrac{y-4}{-5-4}=\dfrac{z-7}{8-7}}$

$\mathsf{\dfrac{x+2}{5}=\dfrac{y-4}{-9}=\dfrac{z-7}{1}}$

$\textsf{It meets yz plane}$

$\mathsf{That\;is\;x=0}$

$\mathsf{\dfrac{2}{5}=\dfrac{y-4}{-9}=\dfrac{z-7}{1}}$

$\implies\mathsf{\dfrac{2}{5}=\dfrac{y-4}{-9}}$

$\implies\mathsf{\dfrac{-18}{5}=y-3}$

$\implies\mathsf{y=\dfrac{-18}{5}+3}$

$\implies\mathsf{y=\dfrac{-3}{5}}$

$\mathsf{and}$

$\mathsf{\dfrac{2}{5}=z-7}$

$\implies\mathsf{z=\dfrac{2}{5}+7}$

$\implies\mathsf{z=\dfrac{37}{5}}$

$\therefore\textsf{The point of intersection is}$

$\mathsf{\left(0,\dfrac{-3}{5},\dfrac{37}{5}\right)}$