UPSC NDA Math Model Paper 8

Given, the equation of two planes ax + by + cz + d = 0 and ax + by + cz + d1 = 0, where d≠d1
Taking the ratio of direction ratios of the plane, we have
⇒

a

a

=

b

b

=

c

c

⇒1=1=1
The ratio of direction ratios of the plane ⇒ax+by+cz+d=0 and ax+by+cz+d1=0 is same
⇒ The plane ax+by+cz+d=0 and ax+by+cz+d1=0 are parallel.
Hence, The two planes ax+by+cz+d=0 and ax+by+cz+d1=0, where d≠d1, have no points in common.