Find the ratio in which line segment jaoining the points A (2, 4, -3) B (-3, 5, 4) is divided by the plane X+Y+Z = 8?3D COORDINATE GEOMETRE

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You should suppose that the plane `x+y+z=8`  divides the line segment joining the points A and B at Q(x,y,z) in the ratio k:1, hence, the coordinates of Q point are:

`((2-3k)/(k+1) , (4+5k)/(k+1), (-3+4k)/(k+1))`

Notice that the point lies in the plane x+y+z=8 such that:

`2 - 3k = 4 + 5k = -3 + 4k`

`-2 = 8k =gt k = -1/4 `

`7 = -k =gt k = -7 `

`5 = 7k =gt k = 5/7 `

Hence, the segment joining A and B divides the plane in the ratio 5:7.

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