Introduction to Three Dimensional Geometry Test

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Introduction to Three Dimensional Geometry Test - 1

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Question 1
1 / -0

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

A
90°

B
60º

C
0°

D
30°

Solution

Explanation:

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 2
1 / -0

The equation xy = 0 in three dimensional space represents

A
a pair of planes at right angles

B
a plane

C
a pair of parallel lines

D
a pair of straight lines

Solution

Explanation:

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 3
1 / -0

The lines, which do not lie in the same plane, are called ?

A
parallel

B
intersecting

C
coincident

D
skew lines

Solution

Explanation:

Lines which lie in same plane can be parallel, coincident or intersecting.

Skew lines are those lines which lie in different planes and never meet to each other
Question 4
1 / -0

The medians of a triangle are concurrent at the point called

A
circumcentre

B
centroid

C
orthocentre

D
incentre

Solution

Explanation:

The centroid is the point of concurrency of the medians of the triangle.it is a point of centre of gravity of triangle
Question 5
1 / -0

The direction cosines of any normal to the XY plane are

A
< 0 , 0 , 1 >

B
< 1 , 0 , 0 >

C
< 1 , 1 , 0 >

D
< 0 , 1 , 0 >

Solution

Explanation:

Concept used - Parellel lines have same direction cosines

Explanation We know Z axis is perpendicular to XY plane and direction cosines of Z axis are <0,0,1>

and as any normal to XY plane will be parallel to Z axis and parellel lines have same direction cosines so answer is <0,0,1>