Three Dimensional Geometry Test

Result

Three Dimensional Geometry Test - 4

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

^{_{The foot of}_from_{on y-axis is}}

A

B

C

D
(0,0,0)
Question 2
1 / -0

The medians of a triangle are concurrent at the point called

A
orthocentre

B
incentre

C
circumcentre

D
centroid

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 perpendicular distance of the point (6, 5, 8) from y–axis is

A
10 units

B
6 units

C
8 units

D
9 units

E
5 units
Question 4
1 / -0

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

A
X-axis

B
Y-axis

C
Z-axis

D
XY-plane
Question 5
1 / -0

The distance of the point ( 3, 4, 5) from X- axis is

A
3

B
5

C
√34

D
√41

Solution

The distance of the point ( 3, 4, 5) from X- axis is
let L be the foot of perpendicular from the point ( 3, 4, 5) to X axis ,then coordinate of L will be (3,0,0) [ because on X axis y and z coordinate are zero]
then distance of the point ( 3, 4, 5) from X- axis i.e. from L (3,0,0) is given by√ (3−3)2+(4−0)2+(5−0)=√ 41
Question 6
1 / -0

How many lines through the origin make equal angles with the coordinate axes ?

A
1

B
8

C
2

D
4

Solution
Question 7
1 / -0

The distance of point (3, 4, 5) from x-axis is

A
3

B
5

C
√ 34

D
√ 41
Question 8
1 / -0

The distance of point A (2, 3, 4) from x-axis is

A
5

B

C
2

D
5

E
None of these
Question 9
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 10
1 / -0

The distance of the point P (a, b, c) from the x-axis is

A

B

C

D
None of these
Question 11
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 90^∘, cos 90^∘>
= < 1 0 0 >
Question 12
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 13
1 / -0

The shortest distance of the point P (a, b, c) form x-axis is

A

B

C

D
None of these
Question 14
1 / -0

The coordinates of the foot of the perpendicular drawn from the point A (1, 0, 3) to the join of the points B (4, 7, 1) and C (3, 5, 3) are

A

B
(5, 7, 17)

C

D
Question 15
1 / -0

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

A
1

B
13

C

D
Question 16
1 / -0

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

A
x

B
y

C
z

D
| z |