THREE DIMENSIONAL GEOMETRY

The end-points of the diagonal of a square are (1,-3,2) and (0,1,3) ,then the length of the diagonal is

• (A).    $\sqrt{13}\$  units

• (B).     $\sqrt{18}$  units

• (C).    4 units

• (D).    3 units

The centroid of the triangle with vertices (5,-6,3) , (2,-2,1) and (2,5,2) is

• (A). (-3,1,2)

• (B). (-3,1,-2)

• (C). (3,1,-2)

• (D). (3,-1,2)

The end-points of a diameter of a sphere are (2,-1,4) and (0,5,-4), then the centre of the sphere is

• (A). (0,0,0)

• (B). (1,-3,4)

• (C). (1,2,0)

• (D). (0,1,2)

The coordinates of a point are (3,0,0), the point lies on

• (A). x - axis

• (b). y - axis

• (C). z - axis

• (D). none of these

The lenght of the perpendicuiar drawn from the point P(3,4,5) on y-axis is

• (A). 10

• (B). $\sqrt{34}$

• (C). $\sqrt{113}$

• (d). $5\sqrt{2}$

The ratio in which the line joining (2,4,5) and (3,5,-9) is divided by the yz-plane is

• (A). 2:3

• (B). 3:2

• (C). -2:3

• (D). 4:-3

The coordinates of the foot of the perpendicular from a point P(6,7,8) on x- axis are

• (A). ( 6,0,0 )

• (B). ( 0, 7 ,0 )

• (C). ( 0, 0 , 8 )

• (D). ( 0 , 7 , 8 )

The point ( -1 , 2 , -3 ) lies in the :

• (A). 7th Octant

• (B). 5th Octant

• (C). 6th Octant

• (D). 8th Octant

Find the locus of a point P which is equidistant from two points ( 1 , 0 , 0 ) and ( -1 , 0 , 0 )

• (A). x=0

• (B). x=1

• (C). x= -1

• (D). x=2

Find a point P on the line segment AB such that P divides AB internally in the ratio 2:1 , where A ( 1 , 2 , 3 ) and B ( -8 , -5 , -3 ).

• (A). ( 5 , 8/3 , 1 )

• (B). ( 5 , - 8/3 , 1 )

• (C). ( 5 , - 8/3 , - 1 )

• (D). ( - 5 , - 8/3 , - 1 )