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:
(,,) 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:
(,, ) So, the coordinates of the required point is
(,,−) Hence, option A is the correct answer