Question

The x-coordinate of a point on the line joining the points Q (2,2,1) and R (5,1,−2) is 4. Find its z-coordinate.

Answer 1

Let the point P divide QR in the ratio k : 1
Now, the coordinate of P is {(5k + 2)/(k + 1), (k + 2)/(k + 1), (-2k + 1)/(k + 1)}
Given, x-coordinate of P is 4
So, (5k + 2)/(k + 1) = 4
=> 5k + 2 = 4(k + 1)
=> 5k + 2 = 4k + 4
=> k = 2
Now, z-coordinate = (-2k + 1)/(k + 1)
                              = (-2*2 + 1)/(2 + 1)
                              = -3/3
                              = -1

Answer 2

Here is your answer ⤵⤵⤵

Let the point P divide QR in the ratio k : 1

Now, the coordinate of P is {(5k + 2)/(k + 1), (k + 2)/(k + 1), (-2k + 1)/(k + 1)}

Given, x-coordinate of P is 4

So, (5k + 2)/(k + 1) = 4

=> 5k + 2 = 4(k + 1)

=> 5k + 2 = 4k + 4

=> k = 2

Now, z-coordinate = (-2k + 1)/(k + 1)

= (-2*2 + 1)/(2 + 1)

= -3/3

= -1

HOPE IT HELPS YOU ☺☺ !!!