Which of the following statments are correct?
1. The coordinates of the point which divides the line segment joining the points
(1,−2,3) and (3,4,−5) internally in the ratio 2:3 is (−3,−14,19).
2. The coordinates of the point which divides the line segment joining the points
(1,−2,3) and (3,4,−5) externally in the ratio 2:3 is (95,25,−15).
None of these
(i) The coordinates of the point p which divides the line segment
joining two points A(x1,y1,z1) and B(x2,y2,z2) internally in the ratio m:n are
(mx2+nx1m+n,my2+ny1m+n,mz2+nz1m+n).
Let P(x,y,z) be the point which divides line segment joining A(1,-2,3)
and B(3,4,-5) internally in the ratio 2:3 therefore,
x=2(3)+3(1)2+3=95
y=2(4)+3(−2)2+3=25
z=2(−5)+3(3)2+3=−15
Thus,thecoordinate of the point p are (95,25,−15).
(ii)Let Q(x,y,z) be the point which divides line segment joining
A(1,−2,3) and B(3,4,−5) externally in the ratio 2:3 is therefore,
Coordinates of point Q(mx2−nx1m−n,my2−ny1m−n,mz2−nz1m−n)
x=2(3)−3(1)2−3=−3
y=2(4)−3(−2)2−3=−14
z=2(−5)−3(3)2−3=19
Thus ,the coordinate of point Q is (-3,-14,19)
So, none of the statements are correct.