VITEEE 2018 Paper

The sphere x2+y2+z2 = 49
has centre at the origin (0, 0, 0) and radius 7.

Disance of the plane
2x + 3y - z - 5 √14 = 0
from the origin
=

|2(0)+3(0)−(0)−5√14|

√22+32+(−1)2

=

|−5√14|

√14

=

5√14

√14

= 5
Thus in Figure; OP = 7, ON = 5
NP2 = OP2 - ON2 = (7)2 - (5)2 = 49 - 25 = 24
∴ NP = 2√6