Three Dimensional Geometry Test

Result

Three Dimensional Geometry Test - 2

Score
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Rank
-
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TIME Taken - -

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Weekly Quiz Competition

Question 1
1 / -0

The point which divides the line joining the points (2, 4, 5) and (3, 5, – 4) in the ratio – 2 : 3 lies in

A
XOY plane

B
YOZ plane

C
ZOX plane

D
None of these
Question 2
1 / -0

The direction cosines of X -axis are

A
< 0 , 1 , 0 >

B
< 1 , 0 , 0 >

C
< 0 , 0 , 1 >

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 3
1 / -0

The direction cosines of any normal to the XY plane are

A
< 1 , 0 , 0 >

B
< 0 , 1 , 0 >

C
< 1 , 1 , 0 >

D
< 0 , 0 , 1 >

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 distance (in units) of the point (1, 2, 3) from X - axis is

A
1

B
13

C
√3

D
√41
Question 5
1 / -0

The distance of the point ( x , y , z ) from xy - plane is

A
x

B
y

C
z

D
| z |