Question

suppose the position vector of X and Y are (1,2,4) and (2,3,5), find the position vector of a point Z that bisect XY in the ratio 2:3

Answer 1

Let`s count out the coordinates of point Z using the formula, where x1, y1, z1 are coordinates of point X, x2, y2, z2 are coordinates of point Y and 2/3 is ratio.

$X_z = (x_1 + 2/3 * x_2) / (1 + 2/3)\\ = (1+ 4/3) / (5/3) =7/3 * 3/5 = 1.4;$

$Y_z = (y_1 + 2/3 * y_2) / (1 + 2/3) \\= (2 + 2/3*3) / (1 + 2/3) = 4 * 3/5 = 12/5 = 2.4;$

$Z_z = (z_1 + 2/3 * z_2) / (1 + 2/3)\\ = (4 + 2/3 * 5) / (1+2/3) = 22/3 * 3/5 = 4.4;$

So, point Z has coordinates (1.4, 2.4, 4.4).