Question

Find the cartesian equation of the line passing through the points $A(3,4,-7)$ and $B(1,-1,6)$.

Answer 1

Equation is castesian form of the line given by

$\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_2}=\frac{z-z_1}{z_2-z_1}$ where $(x_1,y_1,z_1)=(3,4,-7)$ and $(x_2,y_2,z_2)=(1,-1,6)$

$\therefore$ The required equation reduces to,

$\frac{x-3}{1-3}=\frac{y-4}{-1-4}=\frac{z+7}{6+7}$

or, $\frac{x-3}{-2}=\frac{y-4}{-5}=\frac{z+7}{13}$ Ans