If l , m , n are the direction cosines of a line , then
l2 + m2 + n2 = 0
l2 + m2 + n2 = 1
l + m + n = 1
l = m = n = 1
Co - ordinate of a point equidistant from the point (0,0,0), (a,0,0), (0,b,0). (0,0,c) is:
(a/2, b/2, c/2)
(a/4, b/4, c/4)
(a/2, b/4. c/4)
(a,b,c)
The equation of the sphere through x2 + y2 + z2= 4; 2x + 3y + 4z = 7 and (1,2,0) is given by:
x2 + y2 + z2 - 2x - 3y + 4 = 0
x2 + y2 + z2 - 2x - 3y + 4z + 3 = 0
x2 + y2 + z2 - 2x - 3y + 6z + 3 = 0
x2 + y2 + z2 - 2x - 3y +8z + 5 = 0
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
The equation of y - axis is
z = 0
x = 0
y = 0, z = 0
z = 0, x = 0
The direction cosines of x - axis are
<1, 0 , 0 >
<0 , 0 , 1>
<0 , 1 , 0 >
<1, 1 , 1 >
In the space the equation by + cz + d = 0 represents a plane perpendicular to the plane:
YOZ
Z = K
ZOX
XOY
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 ratio in which the line joining (2 , 4 , 5) , (3 , 5 , -9) is divided by the YZ plane is
2 : 3
3 : 2
-2 : 3
4 : - 3
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
