1. The equation x² – x – 2 = 0 in three dimensional space is represented by

2. The distance of the plane 2x – 3y + 6z + 7 = 0 from the point (2, -3, -1) is

3. The direction ratios of the normal to the plane 7x + 4y – 2z + 5 = 0 are

4. Determine the direction cosines of the normal to the plane and the distance from the origin. Plane z = 2

5. Four points (0, -1, -1) (-4, 4, 4) (4, 5, 1) and (3, 9, 4) are coplanar. Find the equation of the plane containing them.

6. The shortest distance between the lines x = y + 2 = 6z – 6 and x + 1 = 2y = -12z is

7. Skew lines are lines in different planes which are

8. The two lines x = ay + b, z = cy + d and = a’ y + b’, z = c’ y + d’ will be perpendicular, iff 

9. The direction cosines of the y-axis are

10. If 2x + 5y – 6z + 3 = 0 be the equation of the plane, then the equation of any plane parallel to the given plane is

11. The equation of the plane passing through the line of intersection of the planes x-2y+3z+8=0 and 2x-7y+4z-3=0 and the point (3, 1, -2) is:​

12.

13. In the following case, determine whether the given planes are parallel or perpendicular, and in case they are neither, find the angles between them. 2x – 2y + 4z + 5 = 0 and 3x – 3y + 6z – 1 = 0

14. If the line joining the origin and the point (–2, 1, 2) makes angle θ1 ,θ2 and θ3 with the positive direction of the coordinate axes, then the value of cos 2θ1 + cos 2θ2 + cos 2θ3 is

15.

16.

17. Find the distance of the point (0, 0, 0) from the plane 3x – 4y + 12 z = 3

18. The equation xy = 0 in three dimensional space is represented by

19. Find the distance of the point (2, 3, – 5) from the plane x + 2y – 2z = 9

20. If a line makes angles Q1, Q21 and Q3 respectively with the coordinate axis then the value of cos² Q1 + cos² Q2 + cos² Q3