Q. 85.0( 1 Vote )

XOZ-plane divides the join of (2, 3, 1) and (6, 7, 1)
A. 3 : 7

B. 2 : 7

C. -3 : 7

D. -2 : 7

Answer :

Given: points A(2, 3, 1) and B(6, 7, 1)


To find: the ratio in which the line joining given points is divided by the XOZ-plane


Formula used:


Section Formula:


A line AB is divided by C in m:n where A(x, y, z) and B(a, b, c).



The coordinates of C is given by,



the y coordinate is always 0 on XOZ-plane


Let Point C(x, 0, z), and C divides AB in ratio k: 1


Therefore, m = k and n = 1


A(2, 3, 1) and B(6, 7, 1)



Coordinates of C using section formula:




On comparing:



7k + 3 = 0(k + 1)


7k + 3 = 0


7k = –3



Hence, C divides AB externally in ratio 3: 7

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