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Question

Ratio in which the xy-plane divides the join of (1, 2, 3) and (4, 2, 1) is
(a) 3 : 1 internally
(b) 3 : 1 externally
(c) 1 : 2 internally
(d) 2 : 1 externally

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Solution

b 3:1 externallySuppose the XY-plane divides the line segment joining the points P 1, 2, 3 and Q 4, 2, 1 in the ratio k:1.Using the section formula, the coordinates of the point of intersection are given byk4+1k+1, k2+2k+1,k1+3k+1The Z-coordinate of any point on the XY-plane is zero.k1+3k+1=0k+3 = 0k=-3=-31Thus, the XY-plane divides the line segment joining the given points in the ratio 3:1 externally.

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