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.
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,
-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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