A point R with x-coordinate 4 lies on the line segment joining the points P(2, - 3, 4) and Q(8, 0, 10). Find the coordinates of the point R

Let the point R (x,y, z) divides PQ in the ratio k:1.⇒k×8+1×2k+1=4⇒8k+2k+1=4⇒8k+2=4k+4⇒8k−4k=4−2⇒4k=2⇒k=12⇒k:1=1:2Hence, the point R divides PQ internally in the ratio 1 : 2.Therefore, y-coordinate of R=1×0+2×(−3)1+2=−63=−2and z-coordinate of R=1×10+2×41+2=10+83=183=6Hence, coordinate of R are (4, -2, 6).