Answer to Question #106339 in Analytic Geometry for Kabiru Mudi

Question

Pls Help *MTH282*
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
A 7i+12j+22k
B. 7i-12j+22k
C.frac{1}{7} (7i+12j+22k)
D.frac{1}{17} (7i-12j+22k)

Answer 1

Division of a line segment in a given ratio is: $x=\frac{x_1+ky_1}{1+k},y=\frac{x_2+ky_2}{1+k},z=\frac{x_3+ky_3}{1+k}$ where

$(x_1,x_2,x_3)$ is$(1,2,4)$ , $(y_1,y_2,y_3)$ is $(2,3,5)$ ,$k=\frac{2}{3}$ ,hence $x=7/5,=12/5,z=22/5$

hence Z= $\frac{1}{5}(7i+12j+22k)$