Introduction To Three Dimensional Geometry CBSE Questions & Answers

There is one and only one sphere through

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 , \(\sqrt 3 \) , 0 ) , C ( 2 , 0 , 0 ) and D ( 1 , 0 , \(\sqrt 3 \)) are the vertices of

The points A ( 0 , 2 , 0 ) , B (\(\sqrt 3 \) , 1 , 0 ) , and C( \({1 \over {\sqrt 3 }},1,{{2\sqrt 2 } \over {\sqrt 3 }}\) ) are the vertices of

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

Area of \(\Delta ABC\) 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 , \(3\hat i + 7\hat j + \hat k,2\hat i + \hat j + \hat k,x\hat i + 3\hat j + \hat k,and4\hat i + y\hat j + \hat k,then\left( {x,y} \right) = \)

If the four points ( 3 , - 2 , - 1 ) , ( 2 , 3 , - 4 ) , ( - 1 , 1 , 2 ) and ( 4 , 5, \(\lambda \)) are coplanar then \(\lambda \) 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