Given info : line segment joining the points A(1, –4, 2) and B(–3, 1, 6) is divided by x-z plane at point P.

To find : the coordinate of point P is ....

solution : Let line segment joining the points A(1, –4, 2) and B(–3, 1, 6) is divided by x-z plane at point P is k : 1.

by section formula,

point P = [(-3k + 1)/(k + 1), (k - 4)/(k + 1) , (6k + 2)/(k + 1)]

at xz plane , y = 0

so, (k - 4)/(k + 1) = 0

⇒k = 4

now, x = (-3k + 1)/(k + 1) = (-3 × 4 + 1)/(4 + 1) = -11/5

z = (6k + 2)/(k + 1) = (6 × 4 + 2)/(k + 1) = 26/5

therefore the coordinate of point P is (-11/5, 0, 26/5)