Introduction to Three Dimensional Geometry Test

Result

Introduction to Three Dimensional Geometry Test - 2

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Question 1
1 / -0

The direction cosines of X -axis are

A
< 0 , 0 , 1 >

B
< 1 , 0 , 0 >

C
< 0 , 1 , 0 >

D
< 0 , 1 , 1 >

Solution

As we know that if a lines makes angles a , b and c with X-axis , Y-axis and Z-axis respectively then direction cosines are given by < cos a , cos b ,cos c >

In our case line is X-axis itself which we know makes angle of 0^∘ , 90^∘ , 90^∘ with X-axis , Y-axis and Z-axis respectively then direction cosine will be

<cos 0^∘ , cos 90^∘, cos 90^∘>

= < 1 0 0 >
Question 2
1 / -0

The medians of a triangle are concurrent at the point called

A
circumcentre

B
incentre

C
centroid

D
orthocentre

Solution

The centroid is the point of concurrency of the medians of the triangle.it is a point of centre of gravity of triangle
Question 3
1 / -0

The direction cosines of any normal to the XY plane are

A
< 1 , 0 , 0 >

B
< 1 , 1 , 0 >

C
< 0 , 0 , 1 >

D
< 0 , 1 , 0 >

Solution

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>
Question 4
1 / -0

the numbers 3, 4 , 5 can be

A
direction cosines of a line in space

B
coordinates of a point on the line y = 4 , z = 0

C
coordinates of a point in the plane x + y – z = 0

D
direction numbers of a line in space

Solution

the numbers 3, 4 , 5 can be direction ratio of any line these not satisfying any other option
Question 5
1 / -0

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

A
parallel

B
intersecting

C
coincident

D
skew lines

Solution

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