Q. 104.0( 2 Votes )

Write the ratio in which the line segment joining (a, b, c) and (-a, -c, -b) is divided by the xy-plane.

Answer :

Given,


The line segment is formed by P and Q points where


Point P = (a,b,c)


Point Q = (-a,-c,-b)



From the figure, we can clearly see that, the line segment joining points P and Q is meeting the plane XY at point G.


Let Point G be (x,y,0) as the z-coordinate on xy plane does not exist.


Also let point G divides the line segment joining P and Q in the ratio m:n.


The coordinates of the point G which divides the line joining points A(x1,y1,z1) and B(x2,y2,z2) in the ratio m:n is given by



Here, we have m:n


x1 = a y1 = b z1 = c


x2 = -a y2 = -c z2 = -b


By using the above formula, we get,




Now, this is the same point as G(x,y,0),


As the x-coordinate is zero,



[Cross Multiplying]


-bm + cn = 0 × (m + n)


-bm + cn = 0


-bm = -cn



Therefore, the ratio in which the plane-XY divides the line joining P & Q is c:b




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