Introduction to Three Dimensional Geometry - Online Test
Q1. The point equidistant from the points ( 0 , 0 , 0 ) , ( 1 , 0 , 0 ) , ( 0 , 2 , 0 ) , and ( 0 , 0 , 3 ) is
Answer : Option B
Explaination / Solution:
let the point equidistant from the points ( 0 , 0 , 0 ) , ( 1 , 0 , 0 ) , ( 0 , 2 , 0 ) , and ( 0 , 0 , 3 ) is (x ,y ,z)
then according to the given condition and distance formula between two points we have
taking ist two expressions and solving them we get
Similarly by taking ist and 3rd we get y = 1 and by taking ist and 4th we get z = 3/2
So the required point is ( 1/2 , 1 , 3/2 )
Q2. The plane x + y = 0 is
Answer : Option D
Explaination / Solution:
No Explaination.
Q3. The points ( 1 , 1 , 0 ) , ( 0 , 1 , 1 ) , ( 1 , 0 , 1 ) , and ( 2/3 , 2/3 , 2/3 ) are
Answer : Option B
Explaination / Solution:
Q4. The lines
Answer : Option A
Explaination / Solution:
No Explaination.
Q5. The lines intersect . The shortest distance between them is
Answer : Option C
Explaination / Solution:
Since the lines intersect.Hence they have a common point in them.hence the distance will be zero
Q6. Volume of a tetrahedron is k X area of one face X length of perpendicular from the opposite vertex upon it, where k is
Answer : Option D
Explaination / Solution:
Volume of tetrahedron 
where a,b,c are co-terminus edges of tetrahedron.a X b is area of one face and c is the perpendicular from the opposite vertex
where a,b,c are co-terminus edges of tetrahedron.a X b is area of one face and c is the perpendicular from the opposite vertex
Q7. A , B C and D are four points in spaces such that AB = BC = CD = DA . Then ABCD is a
Answer : Option B
Explaination / Solution:
It can be square or rhombus(all sides are equal).Angle property must be mentioned.
Q8. The foot of perpendicular from (α,β,γ) on Y axis is
Answer : Option C
Explaination / Solution:
Let P() be the point and Q (0,b,0) be any point on Y axis.
drs of PQ=(
drs of y axis (0,b,0)
Since PQ perpendicular to y axis.hence a1a2+b1b2+c1c2=0
hence the foot of perpendicular will be
Q9. The equation 
represents
represents
Answer : Option D
Explaination / Solution:
The equation 
x=0 , y= , z= 0 which represent Y axis
x=0 , y= , z= 0 which represent Y axis
Q10. The equation 
represents
represents
Answer : Option B
Explaination / Solution:
The equation 
which represent generally XY plane i.e the plane y=0
which represent generally XY plane i.e the plane y=0