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1.
Equation of the plane through three points 
with position vectors 
is
with position vectors is
2.
The equation of the plane in which the lines 
and 
lie, is
and lie, is
3.
The length of the perpendicular from the origin to the plane passing through three non-collinear points 
is
is
4.
The shortest distance from the point 
to the surface of the sphere 
is
to the surface of the sphere is
5.
A plane π makes intercepts 3 and 4 respectively on z-axis and x-axis. If π is parallel to y-axis, then its equation is
6.
A line passes through two points 
and 
The coordinates of a point on this line at a distance of 14 units from 
are
and The coordinates of a point on this line at a distance of 14 units from are
7.
The equation of the perpendicular from the point 
to the plane 
to the plane
8.
The equation of the plane through the points (2, 2, 1) and (9, 3, 6) and perpendicular to the plane 
, is
, is
9.
The perimeter of the triangle with verities at (1,0,0).(0,1,0) and (0,0,1) is
10.
If the distance of the point P 
from the plane 
where 
is 5, then the foot of the perpendicular from P to the plane is
from the plane where is 5, then the foot of the perpendicular from P to the plane is