A point `R` with x-coordinates 4 lies on the line segment joining the points `P(2,-3,4)a n d\ Q(8,0, 10)dot` Find the coordinates of the point `Rdot`

Explanation

Let `R` divides the line joining `P(2,-3,4)` and `Q(8,0,10)` in ratio `k:1`.

The, coordinates of `R(x,y,z) = ((kx_2+x_1)/(k+1),(ky_2+y_1)/(k+1),(kz_2+z_1)/(k+1))`

Here, we are given x-coordinate of `R` that is `4`.
`:. R(4,y,z) = ((8k+2)/(k+1),(0-3)/(k+1),(10k+4)/(k+1))`

`:. (8k+2)/(k+1) = 4=> 8k+2 = 4k+4 => k = 1/2`

So, y-coordinate` = -3/(k+1) = -3/(3/2) = -2`

z-coordinate ` = (10(1/2)+4)/(3/2) = 9/(3/2) = 6`

So, coordinates of point `R` are `(4,-2,6)`.