Answer to Question #202770 in Analytic Geometry for tanya

Question

Let R be the point which divides the line segment joining P(2,1,0) and Q(−1,3,4) into the ratio 1 : 2 such that PR < PQ. Find the equation of the line passing through R and parallel to the line

(x /2) = y = (z/ 2)

Answer 1

Two lines are parallel if the have the same slopes.

Equation of line:

$\frac{x-x_0}{k}=\frac{y-y_0}{l}=\frac{z-z_0}{m}$

$x_R=x_P+(x_Q-x_P)/3$

$y_R=y_P+(y_Q-y_P)/3$

$z_R=z_P+(z_Q-z_P)/3$

Point R=(1, 5/3, 4/3)

Then, the equation of line passing through R and parallel to the given line

$\frac{x-1}{2}=y-5/3=\frac{z-4/3}{2}$