Introduction to Three Dimensional Geometry - Online Test
Q1. The equation xy = 0 in three dimensional space represents
Answer : Option B
Explaination / Solution:
since xy=0 implies x=0 or y=0.i.e YZ plane or XZ plane.Hence it represents a pair of planes at right angles
Q2.
The graph of the equation in the three dimensional space is
Answer : Option B
Explaination / Solution:
No Explaination.
Q3. In three dimensional space, locus of the equation is
Answer : Option D
Explaination / Solution:
No Explaination.
Q4. The distance of the point ( x , y , z ) from the XY –plane is
Answer : Option D
Explaination / Solution:
Let L be the foot of perpendicular segment from the point P (x,y,z) on XY plane
Now since L is the foot of perpendicular on XY plane so z coordinate will be zero so the point L will be (x,y,0)
then distance between these two will be = = |z|
Q5. The angle between the lines x = 1 , y = 2 and y = - 1 , z = 0 is
Answer : Option B
Explaination / Solution:
x = 1 , y = 2 represents XY plane and y = - 1 , z = 0 represents YZ plane.Since XY perpendicular to YZ .hence angle is 90 degrees
Q6. The lines having drs as a1a2+b1b2+c1c2=0 are
Answer : Option C
Explaination / Solution:
Hence lines are perpendicular
Q7. The line x = 1 , y = 2 is
Answer : Option A
Explaination / Solution:
No Explaination.
Q8. The equation ( x – 1 ) ( x – 2 ) = 0 represents , in three dimensional space , a
Answer : Option C
Explaination / Solution:
The equation ( x – 1 ) ( x – 2 ) = 0 represents , in three dimensional space , a pair of parallel planes
( x – 1 ) ( x – 2 ) = 0 => ( x – 1 )=0 , ( x – 2 ) = 0
x =1 and x=2
According to the equation ax +by +cz = d and by the formula we have both the planes represent pair of parallel planes
Q9. A point ( x , y , z ) moves parallel to X- axis . Which of the three variables x , y , z remain fixed ?
Answer : Option C
Explaination / Solution:
A point ( x , y , z ) moves parallel to X- axis then value of x will vary and remaining will be fixed
Q10. A point ( x , y , z ) moves parallel to XY - plane . Which of the three variables x , y , z remain fixed ?
Answer : Option B
Explaination / Solution:
A point ( x , y , z ) moves parallel to XY - plane then x and y -coordinate will vary and z will fixed
