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`

Answer

N/a

Explanation

Here `P-=(2,-3,4) " and" Q-=(8,0,10)` Let x-coordinate of a point R lying on line PQ is 4.
Let the coordinates of point R by (4,y,z) and R divides PQ in the ratio k : 1 .
`therefore 4=(k(8)+1(2))/(k+1)` (from x-coordinate)
`implies 4k+4=8k+2 " " implies k=(1)/(2)`
`therefore` R divides PQ in the ratio 1 : 2.
Now, `y=(1(0)+2(-3))/(1+2)=(-6)/(3)=-2`
and `z=(1(10)+2(4))/(1+2)=(18)/(3)=6`
`therefore` coordinates of point R=(4,-2,6)