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Question

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).


A

Only 1

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B

Only 2

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C

Both 1 & 2

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D

None of these

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Solution

The correct option is D

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(mx2nx1mn,my2ny1mn,mz2nz1mn)

x=2(3)3(1)23=3

y=2(4)3(2)23=14

z=2(5)3(3)23=19

Thus ,the coordinate of point Q is (-3,-14,19)

So, none of the statements are correct.


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