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Q1. The point (3,2,0) lies in the

• XY plane
• YZ plane
• XZ plane
• z axis

Solution

A point whose z coordinate is zero, must lie in the XY plane, x coordinate is zero, must lie in the ZY plane and y coordinate is zero, must lie in the XZ plane.

Q2. The equation representing the set of points which are equidistant from the points (1, 2 , 3) and ( 3 , 2 , -1) is

• x - 2y = 0
• -x + 2y = 0
• 2x - 2y = 0
• x - 2z = 0

Solution

Q3. The coordinates of the vertices of a triangle are (1,2,3),(4,5,6) and (-1,-2,-3).So the centroid is

• (2/3,1/3,5/3)
• (4/3,5/3,6/3)
• (1/2,3/2,5/2)
• (4/3,5/3,1/3)

Solution

For a triangle  with vertices having coordinates ()  , () and (,,), the centroid has coordinates  So substituting the values of the coordinates we get

Q4. The distances of the point (1, 2, 3) from the coordinate axes are A, B and C respectively. Which option is correct?

• B² = 3C²
• A² = B² + C²
• A² = 2C²
• 2A²C² = 13B²

Solution

So, 2A²C² = 13B² are true.

Q5. The equation of the set of points P which is equidistant from the points (0, 2, 3) and (2, –2, 1) is:

• x + 2y + z + 1 = 0
• x – 2y – z – 1 = 0
• x – 2y – z + 1 = 0
• x + 2y – z + 1 = 0

Solution

Q6. Three dimensional coordinate planes divide the space into …… octants.

• four
• six
• eight
• twelve

Solution

A three dimensional coordinate planes divide the space into eight octants.

Q7. A and B be the points (3, 4, 5) and (-1, -3, -7), respectively, the equation of the set of points P such that PA² + PB² = k², where k is a constant will

• Be independent of k
• Have a term  of k to the power 1 only
• Have a term  of k to the power 2 only
• Have a term  of k to the power 1 and another with k to the power 2

Solution

Q8. The points (1, -1, 3), (2, -4, 5) and (5, -13, 11) are:

• Coplanar
• Collinear
• Vertices of a right triangle
• Vertices of a square

Solution

Let the points be represented by A (1, -1, 3), B(2, -4, 5) and C(5, -13, 11). Then by using distance formula We note that AB + BC = CA. Thus, A, B, and C are collinear

Q9. A point (x, y, z) moves parallel to x-axis. Which of the three variables x, y, z remain fixed?

• x
• x and y
• y and z
• z and x

Solution

When a point (x, y, z) moves parallel to X-axis, both Y and Z coordinates remain fixed.

Q10. The coordinates of a point are (0, 3, 1).So the point belongs to

• XY plane
• YZ plane
• XZ plane
• The x axis

Solution

Any point in the three dimensional plane which has its x coordinate equal to zero,  lies in the YZ plane.

Q11. A point has coordinates (0,-3,0), So it lies on the 

• x axis
• y axis
• z axis
• intersection of x and y axes

Solution

Every point of the  type (0,y,0) lies on the y axis. Hence the answer.

Q12. The coordinates point in XY-plane which is equidistant from three points A(2, 0, 3), B(0, 3, 2) and C(0, 0, 1) are:

• (2, 3, 1)
• (1, 2, 3)
• (3, 2, 0)
• (2, 0, 1)

Solution

z-coordinate = 0 on XY-plane Let P(x, y, 0) be a point on XY-plane such that PA = PB = PC

Q13. The ratio in which the line joining the points (a, b, c) and (–a, –c, –b) is divided by the zx plane is:

• c : b
• b : c
• a : b
• a : c

Solution

Let the ratio of the line joining (a, b, c) and (–a, –c, –b) divided by the zx-plane at P is m : 1 Therefore, the co-ordinates of P are,                                                                                 Since the line divided by the zx plane so y = 0 Now, Hence, the ratio are b : c.

Q14. The image of point (5, 2, - 7) in XY plane is:  

• (- 5, 2, -7)
• (- 5, - 2, 7)
• (5, 2, 7)
• (5, 2, - 7)

Solution

The image of point (5, 2,-7) in XY plane is (5, 2, 7).

Q15. The ratio in which the join of points (1, –2, 3) and (4, 2, –1) is divided by XOY plane is:

• 1 : 3
• 3 : 1
• –1 : 3
• – 3 : 1

Solution

: Let A (1, –2, 3) and B (4, 2, –1). Let the plane XOY meet the line AB in the point C such that C divides AB in the ratio k : 1, then . Since C lies on the plane XOY i.e. the plane z = 0, therefore, . Hence the required ratio is 3:1

Q16. Three vertices of a parallelogram PQRS are P(3, - 1, 2), Q (1, 2, - 4) and R (- 1, 1, 2). Find the coordinates of the fourth vertex.

• (1,2,8)
• (-1,-2,8)
• (1,-2,8)
• (1,-2,-8)

Solution

Q17. The ratio, in which YZ-plane divides the line joining (2, 4, 5) and (3, 5, 7) is:

• 1 : 2
• 4:1
• 2 : 3 
• 5 : 4

Solution

Let the line joining (2, 4, 5) and (3, 5, 7) be divided by the yz plane in the ratio m : 1. Therefore the co-ordinates are                                   Since, it divides by YZ-plane i.e x = 0                                                    Hence, ratio are 2 : 3.

Q18. The ratio in which the join of points (1, -2, 3) and (4, 2, -1) is divided by XOY plane is:

• 1 : 3;internally
• 3 : 1; internally
• 3 : 1;externally
• 1 : 3; externally

Solution

Let A (1, -2, 3) and B (4, 2,-1). Let the plane XOY meet the line AB in the point C such that C divides AB in the ratio k : 1, then . Since C lies on the plane XOY i.e. the plane z = 0, therefore, . Hence, the required ratio is 3 : 1.

Q19. A point is on the X-axis, its y-coordinate and z-coordinates are:

• y, z
• 0, 0
• 1, 1
• b, c

Solution

If x-coordinate of a point on X-axis is x, then the coordinates of this point is (x, 0, 0).

Q20. The coordinates of the origin O are (0, 0, 0). The coordinates of any point on the x-axis will be as (x, 0, 0) and the coordinates of any point in the YZ-plane will be as:

• (0, y, z)
• (x, 0, 0)
• (1, y, z)
• (x, 1, 1)

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