Introduction to Three Dimensional Geometry Test

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Introduction to Three Dimensional Geometry Test - 3

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Weekly Quiz Competition

Question 1
1 / -0

The equation xy = 0 in three dimensional space represents

A
a pair of parallel lines

B
a pair of planes at right angles

C
a pair of straight lines

D
a plane

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
Question 2
1 / -0

The graph of the equation x² + y² = 0 in the three dimensional space is

A
Z - axis

B
X - axis

C
Y - axis

D
XY – plane

Solution

x² + y² = 0 ⇒ x = 0 and y = 0 represents a point (0,0) in space in 2D. In 3D the collection of all these points forms Z axis.
Question 3
1 / -0

In three dimensional space, locus of the equation x² + z² = 0 is

A
y - axis

B
a degenerate circle

C
a degenerate sphere

D
empty set

Solution

x² + z² = 0 ⇒ x = 0 and z = 0 it will represent a point in 2d and in 3d the collection of all these point will form Y axis .
Question 4
1 / -0

The angle between the lines x = 1 , y = 2 and y = - 1 , z = 0 is

A
60⁰

B
0⁰

C
30⁰

D
90⁰

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
Question 5
1 / -0

The equation ( x – 1 ) ( x – 2 ) = 0 represents , in three dimensional space , a

A
an empty set

B
pair of parallel planes

C
pair of straight lines

D
sphere

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 a1/a2 = b1/b2 = c1/c2 we have both the planes represent pair of parallel planes
Question 6
1 / -0

A point ( x , y , z ) moves parallel to X- axis . Which of the three variables x , y , z remain fixed ?

A
x

B
z and x

C
x and y

D
y and z

Solution

A point ( x , y , z ) moves parallel to X- axis then value of x will vary and remaining will be fixed
Question 7
1 / -0

A point ( x , y , z ) moves parallel to XY - plane . Which of the three variables x , y , z remain fixed ?

A
x

B
y

C
z

D
x and y

Solution

A point ( x , y , z ) moves parallel to XY - plane then x and y -coordinate will vary and z will fixed

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Introduction to Three Dimensional Geometry Test - 3

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Introduction to Three Dimensional Geometry Test - 3

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Question 1

a pair of parallel lines

a pair of planes at right angles

a pair of straight lines

a plane

Solution

Question 2

Z - axis

X - axis

Y - axis

XY – plane

Solution

Question 3

y - axis

a degenerate circle

a degenerate sphere

empty set

Solution

Question 4

600

00

300

900

Solution

Question 5

an empty set

pair of parallel planes

pair of straight lines

sphere

Solution

Question 6

x

z and x

x and y

y and z

Solution

Question 7

x

y

z

x and y

Solution

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60⁰

0⁰

30⁰

90⁰