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 angle between the planes 2x - y + z = 6 and x + y + 2z = 7 is
π/4
π/6
π/3
π/2
For every P(x,y,z) on the XY - plane:
x = 0
y = o
z = 0
none of these
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
The direction cosines of x - axis are
<1, 0 , 0 >
<0 , 0 , 1>
<0 , 1 , 0 >
<1, 1 , 1 >
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 sphere whose centre is (1,1,1) and which passes through (3,3,2), is:
x2 + y2 + z2 + 2x + 2y + 2z = 6
x2 + y2 + z2 - 2x - 2y +- 2z = 0
x2 + y2 + z2 - 2x + 2y - 2z = 6
x2 + y2 + z2 + 2x + 2y + 2z = 38
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
The equation of y - axis is
y = 0, z = 0
z = 0, x = 0
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 >