Show that the plane ax+by+cz+d=0divides the line joining the points (x

1.	Show that the plane ax+by+cz+d=0divides the line joining the points (x1,y1,z1)and(x2,y2,z2) in the ratio −ax1+by1+cz1+dax2+by2+cz2+d.
Answer» Show that the plane $a x + b y + c z + d = 0$ divides the line joining the points $(x_{1}, y_{1}, z_{1}) a n d (x^{2}, y^{2}, z^{2})$ in the ratio $- \frac{a x_{1} + b y_{1} + c z_{1} + d}{a x_{2} + b y_{2} + c z_{2} + d}$ .

Show that the plane ax+by+cz+d=0divides the line joining the points (x1,y1,z1)and(x2,y2,z2) in the ratio −ax1+by1+cz1+dax2+by2+cz2+d.

Answer»

Show that the plane $a x + b y + c z + d = 0$ divides the line joining the points

$(x_{1}, y_{1}, z_{1}) a n d (x^{2}, y^{2}, z^{2})$ in the ratio

$- \frac{a x_{1} + b y_{1} + c z_{1} + d}{a x_{2} + b y_{2} + c z_{2} + d}$ .