Let the line segment formed by joining the points (−1,3,6) and (2,−4,7) is divided by the YZ plane in the ratio k:1 at the point P, then the co-ordinates of P are
(2k−1k+1,−4k+3k+1,7k+5k+1)
But P lies in the YZ plane,
∴x−co-ordinate is zero
⇒2k−1k+1=0
⇒2k−1=0
⇒2k=1
⇒k=12
Hence,YZ plane divides the line segment AB in the ratio 11:1
i.e.,1:2 internally and the coordinates of the point of division are
⎛⎜
⎜
⎜⎝2×12−112+1,−4×12+312+1,7×12+512+1⎞⎟
⎟
⎟⎠
or ⎛⎜
⎜
⎜⎝1−112+1,−2+31+22,7+1021+22⎞⎟
⎟
⎟⎠
or (0,23,173)