Q. 44.0( 51 Votes )
Let the point P divides AB in the ratio k : 1.
Comparing this information with the details given in the question, we have
x1 = 2, y1 = -3, z1 = 4; x2 = -1, y2 = 2, z2 = 1 and m = k, n = 1
By section formula,
We know that the coordinates of the point R which divides the line segment joining two points P (x1, y1, z1) and Q (x2, y2, z2) internally in the ratio m : n is given by:
So, we have,
The coordinates of P =
Now, we check if for some value of k, the point coincides with the point C.
⇒ -k + 2 = 0 ⇒ k = 2
When k =2, then
Therefore, C is a point which divides AB in the ratio 2 : 1 and is same as P.
Hence, A, B, C are collinear.
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