The equation of the sphere touching the three co-ordinates planes is:
x2 + y2 + Z2 + 2a (x+y+Z) + 2a2 = 0
x2 + y2 + Z2 - 2a (x+y+Z) + 2a2 = 0
x2 + y2 + Z2 ± 2a (x+y+Z) + 2a2 = 0
x2 + y2 + Z2 ± 2 ax ± 2ay ± 2aZ + 2a2 = 0
The co-ordinates of a point equidistant from four distinct point (0,0,0), (a,0, 0), (0,b,0) and (0,0,c) are:
(a/2, b/2. c/2)
(a,b,c)
(a/3, b/3. c/3)
The points A (4,5,1), B (0,-1,-1) ,C(3,9,4) and D (-4,4,4) are:
Collinear
Coplanar
Non - coplanar
non collinear and non coplanar
In the space the equation by + cz + d = 0 represents a plane perpendicular to the plane:
YOZ
Z = K
ZOX
XOY
In three dimensional space, the path of a point whose distance from the x axis is 3 times its distance from the yz plane is:
y2 + z2 = 9x2
x2 + y2 = 3z2
x2 + z2 = 3y2
y2 - z2 = 9x2
Which of the following triplets gives the direction cosines of a line ?
<1 , 1 , 1 >
<1 , -1 , 1 >
<1 , -1 , -1 >
<1/√3 , 1/√3 ,1/√3 >
Under what condition does a straight line is parallel to the xy -plane?
l = 0
m = 0
n = 0
l = 0, m = 0
The xy- plane divides the line joining the points (-1,3,4) and (2,-5,6):
internally in the ratio 2:3
internally in the ratio 3:2
externally in the ratio 2:3
externally in the ratio 3:2
A straight line with direction cosines (0,1,0) is:
Parallel to the x - axis
Parallel to the y - axis
Parallel to the z- axis
Equally inclined to all the axis
The equation of the XOY plane is
x = 0
y = 0
z = 0
z = c, c ≠ 0
