HSC Line And Plane All solved MCQ's: Maharashtra Board

• NCERT Three Dimensional Geometry
• This MCQs are based on the Mathematics Part I Textbook of Maharashtra (click here for reference).

Line And Plane

Q.1. The vector equation of line 2x-1=3y+2=z-2 is

(A) 

(B) 

(C) 

(D) 

Q.2. The perpendicular distance of the plane 2x+3y-z=k from the origin is  units, the value of k is 

(A) 14

(B) 196

(C) 

(D) 

Q.3. The angle between the planes and  is

(A) 

(B) 

(C) 

(D) 

Q.4. The direction ratios of the line which is perpendicular to the two lines 

(A) 4, 5, 7

(B) 4, -5, 7

(C) 4, -5, -7

(D) -4, 5, 8

Q.5. The lines  are coplanar if

(A) k=1 or -1

(B) k=0 or -3

(C) k=

(D) k=0 or -1

Q.6. The lines  and are

(A) perpendicular

(B) intersecting

(C) skew

(D) coincident

Q.7. The shortest distance between the lines  is

(A) 

(B) 

(C) 

(D) 3

Q.8. If the point  lies on the line  then the value of  is _______.

(A) -1

(B) 1

(C) 8

(D) -8

Q.9. The acute angle between the two planes x + y + 2z = 3 and 3x - 2y + 2z =7 is_______.

(A) 

(B) 

(C) 

(D) 

Q.10. The acute angle between the line  and the plane 10x + 2y - 11z = 8 is _______.

(A) 

(B) 

(C) 

(D) 

Q.11. If the line,  meets the plane, x + 2y + 3z = 15 at a point P, then the distance of P from the origin is

(A) 

(B) 

(C) 

(D) 

Q.12. A plane passing through the points (0, -1, 0) and (0, 0, 1) and making an angle  with the plane y - z + 5 = 0, also passes through the point:

(A) 

(B) 

(C) 

(D)  

Q.13. The direction ratios of the line 3x+1=6y-2=1-z are

(A) 2, 1, 6

(B) 2, 1, -6

(C) 2, -1, -6

(D) -2, 1, 6

Q.14. The foot of perpendicular drawn from the point (0, 0, 0) to the plane is (4, -2, -5) then the equation of the plane is

(A) 4x + y + 5z = 14

(B) 4x - 2y - 5z = 45

(C) x - 2y - 5z = 10

(D) 4x + y + 6z = 11

Q.15. The length of the perpendicular from(1, 6, 3) to the line 

(A) 3

(B) 

(C) 

(D) 5

Q.16. If the line  is perpendicular to the line  then the value of k is:

(A) 

(B) 

(C) 

(D) 

Q.17. The shortest distance between the lines  is

(A) 

(B) 

(C) 

(D) 

Q.18. Equation of X-axis is

(A) x=y=z

(B) y=z

(C) y=0, z=0

(D) x=0, y=0

Q.19. The equation of the plane passing through the points (1, -1,1), (3, 2, 4) and parallel to Y-axis is:

(A) 3x+2z-1=0

(B) 3x-2z=1

(C) 3x+2z+1=0

(D) 3x=2z=2

Q.20. The angle between the lines 2x=3y=-z and 6x=-y=-4z is

(A) 

(B) 

(C) 

(D) 

Q.21. The equation of the plane passing through (2, -1, 3) and making equal intercepts on the coordinate axis is

(A) x+y+z=1

(B) x+y+z=2

(C) x+y+z=3

(D) x+y+z=4

Q.22. the direction cosines of the normal to the plane 2x-y+2z=3 are

(A) 

(B) 

(C) 

(D) 

Q.23. The equation of the plane in which the line  lie, is

(A) 17x - 47y - 24z + 172 = 0

(B) 17x + 47y - 24z + 172 = 0

(C) 17x + 47y + 24z + 172 = 0

(D) 17x - 47y + 24z + 172 = 0

Q.24. If the line  lies in the plane 3x - 14y + 6z +49 = 0, then the value of m is:

(A) 5

(B) 3

(C) 2

(D) -5

Q.25. If the planes  are parallel , then the values of  are respectively.

(A) 

(B) 

(C) 

(D) 

Q.26. Measure of angle between the planes 5x-2y+3z-7=0 and 15x-6y+9z+5=0 is

(A) 

(B) 

(C) 

(D) 

Q.27. If the lines given by  are perpendicular, then the value of m is

(A) 

(B) 

(C) 

(D)