Three Dimensional Geometry Test

Result

Three Dimensional Geometry Test - 6

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

Which of the following statements regarding the three pairs of lines is/are correct?

(i) (ii) and ⁽ⁱⁱⁱ⁾

A
(i) and (ii) are skew lines.

B
(ii) and (iii) are coplanar lines.

C
(i) represents skew lines and (ii) represents coplanar lines.

D
(i), (ii) and (iii) are coplanar lines.
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 straight lines

D
a pair of parallel lines

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 3
1 / -0

If and are the roots of the quadratic equation ax² + bx + c = 0 and the plane is passing through the line of intersection of the two planes and , then the value of b is

A
a negative number

B
zero

C
a positive number

D
Cannot be determined
Question 4
1 / -0

If the plane 2ax - 3ay + 4az + 6 = 0 passes through the mid-point of the line joining the centres of the spheres x² + y² + z² + 6x - 8y - 2z = 13 and x² + y² + z² - 10x - 4y - 2z = 8, then a equals

A
3/2

B
-1/2

C
-1

D
1
Question 5
1 / -0

The distance of the point ( x , y , z ) from the XY –plane is

A
|z|

B
z

C
y

D
x

Solution

Let L be the foot of perpendicular segment from the point P (x,y,z) on XY plane
Now since L is the foot of perpendicular on XY plane so z coordinate will be zero so the point L will be (x,y,0)
then distance between these two will be √(x−x)²+(y−y)²+(z−0)² =√ z² = |z|
Question 6
1 / -0

Equation of the sphere which circumscribes the tetrahedron with vertices O (0, 0, 0), A (1, 0, 0), B (0, 1, 0), C (0, 0, 1) is

A
x² + y² + z² + x + y + z = 0

B
x² + y² + z² - x - y - z = 0

C
x² + y² + z² + 2 x + 2 y + 2 z = 0

D
none of these.
Question 7
1 / -0

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

A
a degenerate circle

B
a degenerate sphere

C
empty set

D
y - axis

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 8
1 / -0

Directions: The following question has four choices, out of which ONE or MORE is/are correct.

If a³ + za² + ya + x = 0, b³ + zb² + yb + x = 0 and c³ + zc² + yc + x = 0, which of the following statements is/are wrong?

A
x = – abc

B
x = ab + bc + ca

C
x = – (a + b + c)

D
None of these
Question 9
1 / -0

Directions: The following question has four choices, out of which ONLY ONE is correct.

An equilateral triangle ABC has each side of length `1` unit. Let M and N be two points respectively on the sides AB and AC such that and If and are orthogonals, the value of K is equal to

A

B

C

D
Question 10
1 / -0

Directions: The following question has four choices, out of which ONE or MORE are correct.

Let PM be a perpendicular from the point P (1, 2, 3) to x-y plane. If OP makes an angle with the positive direction of z-axis and OM makes an angle with the positive direction of x-axis, where O is the origin (and are acute angles), then

A

B

C
tan = 2

D
Question 11
1 / -0

The equation of sphere concentric with the sphere x² + y² + z² – 4x – 6y – 8z – 5 = 0 and which passes through origin is

A
x² + y² + z² = 0

B
x² + y² + z² – 6y – 8z = 0

C
x² + y² + z² – 4x – 6y – 8z = 0

D
None of these
Question 12
1 / -0

If P (x, y, z) is a point on the line segment joining Q (2, 2, 4) and R (3, 5, 6) such that projections ofon the axes are, respectively, then in what ratio does P divide ?

A
1 : 2

B
3 : 2

C
2 : 3

D
1 : 3
Question 13
1 / -0

The equation of the sphere circumscribing the tetrahedron whose faces are x = 0, y = 0, z = 0 and is

A
x² + y² + z² = k² = a² + b² + c²

B
x²+ y² + z² - ax - by - cz = 0

C
x² + y² + z² - 2 ax - 2 by - 2 cz = 0

D
none of these.
Question 14
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=0andy=0 represents a point (0,0) in space in 2D. In 3D the collection of all these points forms Z axis
Question 15
1 / -0

Directions: The following question has four choices, out of which ONLY ONE is correct.

A force of unit acts along the line . The moment of this force about the point (4, 1) along positive z - axis is

A
0

B
5

C
- 5

D
None of these
Question 16
1 / -0

The distance of the point (1, 0, – 3) from the plane x – y – z = 9 measured parallel to the line = = is

A
6 units

B
5 units

C
8 units

D
7 units
Question 17
1 / -0

The radius of the circle in which the sphere x² + y² + z² + 2x - 2y - 4z - 19 = 0 is cut by the plane x + 2y + z + 7 = 0 is

A
2

B
3

C
4

D
1
Question 18
1 / -0

Let AB be the straight line . From a point P (1, 2, 5), a straight line PQ is drawn parallel to the plane 3x + 4y + 5z = 0 to meet AB in Q. Then, the equation of PQ is

A

B

C

D
Question 19
1 / -0

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

A
90⁰

B
30⁰

C
60⁰

D
0⁰

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