UPSC NDA Math Model Paper 3

Here, we have to find the coordinates of the point which divides the line segment joining the point A (1, - 2, - 3) and B (3, 4, - 5) in the ratio 2 : 3 internally.
As we know that, if a point C divides the line segment joining the points A(x1,y1,z1) and B(x2,y2,z2) in the ratio m : n internally then coordinates of point C is given by: (

mx2+nx1

m+n

,

my2+ny1

m+n

,

mz2+nz1

m+n

)
Here, m=2,n=3,x1=1,y1=−2,z1=−3, x2=3,y2=4 and z2=−5
So, the coordinates of the required point is: (

2×3+3×1

2+3

,

2×4+3×(−2)

2+3

,

2×(−5)+3×(−3)

2+3

)
So, the coordinates of the required point is (

9

5

,

2

5

,−

19

5

)
Hence, option A is the correct answer