Introduction to 3-D Geometry, Class 12 Mathematics NCERT Solutions

1. There will be total 20 MCQ in this test.
2. Please keep a pen and paper ready for rough work but keep your books away.
3. The test will consist of only objective type multiple choice questions requiring students to mouse-click their correct choice of the options against the related question number.
4. No negative marking for incorrect choice.
5. Please click on “Finish the Test” when you want to exit.
6. All the best – Happy Studying.

1. Find the direction cosines of a line which makes an angle with all three the coordinate axes.

± 1/√2

1/√3

1/√2

± 1/√3

Question 1 of 20

2. Three planes, viz the XY Plane, XZ Plane and the YZ Plane divide the space into eight parts. Each part is called an OCTANT. What is the relation between these three planes

They form the angles α, β & γ with each other

Any two must be perpendicular to each other.

All three are mutually perpendicular

no relation between these three planes

Question 2 of 20

3. The co-ordinates of the vertices of the triangle are A(-2, 3, 6), B(-4, 4, 9) and C(0, 5, 8). The direction cosines of the median BE are:

1 , 0 , -2/3

3/√13, 0, -2/√13

3/4, 0, -2/4

-3/√12, 0, -2/√13

Question 3 of 20

4. If the direction cosines of a line from the positive X-axis and Y-axis are

The angle of the line through Z-axis is:

30°

45°

135°

60°

Question 4 of 20

5. The direction cosines of the line equally inclined with the axes are:

1, 1, 1

1/√3, 1/√3, 1/√3

1, 0, 0

1/3, 1/3, 1/3

Question 5 of 20

6. The direction cosines of the line whose direction ratios are 6, – 6, 3 are:

Question 6 of 20

7. Find the direction cosines of the x axis.

1, 0, 0

0, 0, 0

0, 1, 0

0, 0, 1

Question 7 of 20

8. The direction cosines of the line joining the points (2, -1, 8) and (-4, -3, 5) are:

Question 8 of 20

9. What are direction numbers of a line.

numbers which are proportional to the direction cosines of a line

numbers which are proportional to the direction cosines of a line.

numbers which are same as direction angles of a line

numbers which are proportional to the direction angles of a line

Question 9 of 20

10. What are direction ratios of a line.

numbers which are proportional to the direction angles of a line

numbers which are proportional to the direction cosines of a line

numbers which are same direction angles of a line

numbers which are proportional to the direction cosines of a line

Question 10 of 20

11. Find the direction cosines of the side AB of the triangle whose vertices are A(3, 5, -4), B(-1, 1, 2) and C(-5, -5, -2)

Question 11 of 20

12. If l, m , n are the direction cosines of any line, then sum of the squares of the direction cosines of the line is always

-1

√3

Question 12 of 20

13. If a line has the direction ratios -4, 18, -12 then what are its direction cosines?

-2, 9, -6

-4, 18, -12

2/11, 9/11, 6/11

-2/11, 9/11, -6/11

Question 13 of 20

14. The direction cosines of the line equally inclined with the axes, are:

1, 1, 1,

0, 0, 0

1/3, 1/3, 1/3

1/√3, 1/√3, 1/√3

Question 14 of 20

15. If a line makes angles 45°,150°, 135°, with x, y and z-axes respectively, find its direction cosines.

Question 15 of 20

16. Find the equation of the set of points which are equidistant from the points (1, 2 , 3) and (3, 2, -1)

x + 2z = 0

y + 2z = 0

x – 2y = 0

x – 2z = 0

Question 16 of 20

17. If a line in the ZX-plane makes an angle 60o with Z-axis, the direction cosines of this line are:

Question 17 of 20

18. A line makes angles α, β, γ with the positive directions of X-axis, Y-axis and Z-axis, respectively, then the directions cosines of the line are:

Question 18 of 20

19. The signs of the X,Y and Z coordinates of a point that lies in the octant OXYZ’ is

(- , + , +)

(-, – , +)

( + , – , -)

( + , + , -)

Question 19 of 20

20. If a line in the ZX-plane makes an angle 30o with Z-axis, the direction cosines of this line are:

Question 20 of 20