A variable plane is at a constant distance h from the origin and meets the coordinate axes in A, B, C. Locus of centroid of ABC is
x2 + y2 + z2 = h- 2
x2 + y2 + z2 = 4h- 2
x2 + y2 + z2 = 16h2
The direction ratios of normal to the plane passing through (0, 0, 1), (0, 1, 2) and (1, 0, 3) are
(2, 1, - 1)
(1, 0, 1)
(0, 0, - 1)
(1, 0, 0)
In the space the equation by + cz + d = 0 represents a plane perpendicular to the
YOZ-plane
ZOX-plane
XOY-plane
None of these
A plane x passes through the point (1, 1, 1). If b, c, a are the direction ratios of a normal to the plane, where a, b, c (a < b < c) are the factors of 2001, then the equation of plane is
29x + 31y + 3z = 63
23x + 29y - 29z = 23
23x + 29y + 3z = 55
31x + 37y + 3z = 71
If the plane 7x + 11y + 13z = 3003 meets the co-ordinate axes in A, B, C, then the centroid of the is
(143, 91, 77)
(143, 77, 91)
(91, 143, 77)
(143, 66, 91)
If a,b, c are three non-coplanar vectors, then the vector equation represents a :
straight line
plane
plane apssing through origin
sphere
If a,b, c are three vectors such that and the angle between is , then
a2 = b2 + c2
b2 = c2 + a2
c2 = a2 + b2
2a2 - b2 = c2
A.
a2 = b2 + c2