Three Dimensional Geometry Test - 5

The distance between the planes    = p₁ and     = p₂ is

The point equidistant from the points (0 , 0 , 0) , (1 , 0 , 0) , (0 , 2 , 0) , and (0 , 0 , 3) is

The plane x + y = 0 is

The points (1 , 1 , 0) , (0 , 1 , 1) , (1 , 0 , 1) , and (2/3 , 2/3 , 2/3) are

The lines The lines    and  

The lines  l₁   and l₂  intersect. The shortest distance between them is

Volume of a tetrahedron is k X area of one face X length of perpendicular from the opposite vertex upon it, where k is

A, B, C and D are four points in spaces such that AB = BC = CD = DA. Then ABCD is a

The foot of perpendicular from (α,β,γ) on Y axis is

The centre of the sphere , which passes through (a , 0 , 0) , (0 , b , 0) (0 , 0 , c) and (0 , 0 ,0) is abc  ≠ 0

A sphere through three non –collinear points A, B, and C is smallest when its centre is

Three planes x + y = 0, y + z = 0, and x + z = 0

The centre of the sphere through the points (0 , 3 , 4) , (0 , 5 , 0) , (4 , 0 , 3) and (- 3 , 4 , 0) is

The points A (0 , 0 , 0) , B (1 , √3  , 0) , C (2 , 0 , 0) and D (1 , 0 , √3) are the vertices of

The points A (0 , 2 , 0) , B (√3  , 1 , 0) ,  are the vertices of

The locus of a first degree equation in x, y, z is a

Area of  ΔABC whose vertices A (- 1 , 2 , 3) , B (1, 1, 1) , and C (2 , - 1 , 3) is

The value of x for which the points (x , x , x) , (0 , - 1 , - 2) , (- 3 , - 4 , - 5) and (- 6 , - 7 , - 8) are non-coplanar is

G is the centroid of triangle ABC. If P.V. of the points G , A , B , C are respectively,   and   then (x, y) = 

If the four points (3 , - 2 , - 1) , (2 , 3 , - 4) , (- 1 , 1 , 2) and (4 , 5, λ) are coplanar then  λ is equal to

The number of spheres of a given radius which touch the coordinate planes is

The plane XOZ divides the join of (1 , -1 , 5) and (2 , 3 ,4) in the ratio k : 1, then the value of k is

In a three dimensional space, the equation 3x –4y = 0 represents

The coordinates of the foot of perpendicular from the point A (1, 1 , 1) , on the line joining the points B (1 , 4 , 6) and C (5 , 4 , 4) are

The points (1, 2 , 3) , (- 1, -1 , - 1) and (3, 5 , 7) are the vertices of