Suppose that the point  R lies on the line segment joining the points P(2, -3, 4) and 0(8, 0, 10) with x-co ordinate 6. Then distance of, R from origin is

Suppose R divides PQ in the ratio k : 1. ∴ R≡8k+2k+1,−3k+1,10k+4k+1It is given that the x--coordinate of point R is 6. ∴ 8k+2k+1=6⇒8k+2=6k+6⇒ 2k=4⇒k=2Therefore, the coordinates of point R are given by6,−32+1,10×2+42+4≡(6,−1,4)