Question

The ratio in which the plane $4x+5y-3z=8$ divides the line joining the points $(-2,1,5)$ and $(3,3,2)$ is

• A. $2:1$
• B. $1:2$
• C. $-2:1$
• D. $3:2$

Answer 1

The correct option is A $2:1$

We know that the ratio in which the plane $ax+by+cz+d=0$ divides the line segment joining ($x_1,y_1,z_1$) and ($x_2,y_2,z_2$) is

$\begin{array}{c}\frac{-\left(a{x}_1+b{y}_1+c{z}_1+d\right)}{a{x}_2+b{y}_2+c{z}_2+d}\\ a=4;b=5;c=-3;d=-8;x_1=-2;y_1=1;z_1=5;x_2=3;y_2=3;z_2=2\\ so,therequiredratio=\frac{-\left(4\left(-2\right)+5\left(1\right)-3\left(5\right)-8\right)}{4\left(3\right)+5\left(3\right)-3\left(2\right)-8}\\ =\frac{-\left(-8+5-15-8\right)}{12+15-6-8}\\ =\frac{26}{13}\\ =\frac{2}{1}\\ or\\ 2:1\end{array}$