Q10 of 84 Page 28

Show that the plane ax + by + cz + d = 0 divides the line joining the points (x1, y1, z1) and (x2, y2, z2) in the ratio .

Given: A(x1, y1, z1) and B(x2, y2, z2)


To prove: the ratio in which the line segment AB is divided by the plane ax + by + cz + d = 0 is


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,



Let C(x, y, z) be any point on given plane and C divides AB in ratio k: 1



Therefore, m = k and n = 1


A(x1, y1, z1) and B(x2, y2, z2)


Coordinates of C using section formula:




On comparing:



Since, ax + by + cz + d = 0







The plane divides AB in the ratio


Hence Provedco


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