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Applications of Vector Algebra - Choose the correct answer | 12th Mathematics : UNIT 6 : Applications of Vector Algebra

Chapter: 12th Mathematics : UNIT 6 : Applications of Vector Algebra

Choose the correct answer

Choose the correct or the most suitable answer from the given four alternatives, Multiple choice questions with answers - Maths Book back 1 mark questions and answers with solution for Exercise Problems

Choose the correct or the most suitable answer from the given four alternatives :

 

1. If and are parallel vectors, then [ ] is equal to

(1) 2

(2) -1

(3) 1

(4) 0


 

2. If a vector  lies in the plane of  and , then


Ans: (3)


 

3. If  = 0, then the value of [ ] is


(3) 1

(4) -1

Ans: (1)


 

4. If , are three unit vectors such that  is perpendicular to  , and is parallel to  then  x ( x  ) is equal to

(1) 

(2) 

(3) 

(4) 

Ans: (2)


 

5. If [] = 1, then the value of  is

(1) 1

(2) -1

(3) 2

(4) 3


 

6. The volume of the parallelepiped with its edges represented by the vectors iˆ + ˆj, iˆ + 2 ˆj, iˆ + ˆj + π kˆ is

(1) π/2

(2) π/3

(3) π

(4) π/4


 

7. If  and  are unit vectors such that [ Ã—  ] = Ï€/4, then the angle between and  is

(1) π/6

(2) π/4

(3) π/3

(4) π/2


 

8. If  and ( Ã—  )×  = λ + μ, then the value of λ + μ is

(1) 0

(2) 1

(3) 6

(4) 3


 

9. If , ,  are non-coplanar, non-zero vectors such that [, ,   ] = 3, then  is equal to

(1) 81

(2) 9

(3) 27

(4)18


 

10. If , are three non-coplanar vectors such that  Ã—( Ã—  ) =  , then the angle between  and  is

(1) π/2

(2) 3Ï€/4

(3) π/4

(4) π


 

11. If the volume of the parallelepiped with  Ã— , Ã—  Ã—  as coterminous edges is 8 cubic units, then the volume of the parallelepiped with ( Ã—  )×( Ã—  ), ( Ã—  ) ×( Ã— ) and ( Ã— ) ×( Ã—  ) as coterminous edges is,

(1) 8 cubic units

(2) 512 cubic units

(3) 64 cubic units

(4) 24 cubic units


 

12. Consider the vectors  such that (×  ) ×( Ã—  ) = 0 . Let P1 and P2 be the planes determined by the pairs of vectors  and  respectively. Then the angle between P1 and P2 is

(1) 0Ëš

(2) 45Ëš

(3) 60Ëš

(4) 90Ëš


 

13. If  Ã—( Ã— ) = ( Ã—  ) × , where  are any three vectors such that  .  â‰  0 and  .  â‰  0 ,then  and  are

(1) perpendicular

(2) parallel

(3) inclined at an angle π/3

(4) inclined at an angle π/3


 

14. If  = 2ˆi + 3ˆ j - ˆk = iˆ + 2 ˆj - 5kˆ,  = 3ˆi + 5 ˆj - ˆk, then a vector perpendicular to  and lies in the plane containing  and  is

(1) -17iˆ + 21 ˆj - 97kˆ

(2) 17iˆ + 21 ˆj -123kˆ

(3) -17iˆ - 21 ˆj + 97kˆ

(4) -17iˆ - 21 ˆj - 97kˆ


 

15. The angle between the lines  is

(1) π/6

(2) π/4

(3) π/3

(4) π/2


 

16. If the line  lies in the plane x + 3y - α z + β = 0, then (α , β ) is

(1) (-5, 5)

(2) (-6, 7)

(3) (5, -5)

(4) (6, -7)


 

17. The angle between the line  = (ˆ i + 2 ˆ j - 3 ˆ k ) + t(2 ˆ i + ˆ j - 2 ˆ k ) and the plane  = (ˆ i + ˆ j) + 4 = 0 is

(1) 0Ëš

(2) 30Ëš

(3) 45Ëš

(4) 90Ëš


 

18. The coordinates of the point where the line  = (6 ˆ i - ˆ j - 3 ˆ k ) + t(-ˆ i + 4 ˆ k ) meets the plane .( ˆ i + ˆ j - ˆ k ) = 3 are

(1) (2,1, 0)

(2) (7, -1, -7)

(3) (1, 2, -6)

(4) (5, -1,1)


 

19. Distance from the origin to the plane 3x - 6 y + 2z + 7 = 0 is

(1) 0

(2) 1

(3) 2

(4) 3


 

20. The distance between the planes x + 2 y + 3z + 7 = 0 and 2x + 4 y + 6z + 7 = 0 is

(1) √7 / 2√2

(2) 7/2

(3) √7 / 2

 (4) 7 / 2√2


 

21. If the direction cosines of a line are  then

(1) c = ±3

(2) c = ±√3

(3) c > 0

(4) 0 < c < 1


 

22. The vector equation points  = (ˆ i - 2 ˆ j - ˆ k ) + t(6 ˆ i - ˆ k ) represents a straight line passing through the

 (1) (0, 6, -1) and (1, -2, -1)

(2) (0, 6, -1) and (-1, -4, -2)

(3) (1, -2, -1) and (1, 4, -2)

(4) (1, -2, -1) and (0, -6,1)


 

23. If the distance of the point (1,1,1) from the origin is half of its distance from the plane x + y + z + k = 0 , then the values of k are

(1) ±3

(2) ±6

(3) -3, 9

(4) 3, -9


 

24. If the planes .(2 ˆi - λ ˆj + ˆk ) = 3 and .(4 ˆi + ˆj - μ ˆk ) = 5 are parallel, then the value of λ and μ are

(1) 1/2 , -2

(2) –1/2 ,2

(3) – 1/2 , -2

(4) 1/2 ,2


 

25. If the length of the perpendicular from the origin to the plane 2x + 3y + λ z = 1 , λ > 0 is 1/5 , then the value of λ is

(1) 2√3

(2) 3√2

(3) 0

(4) 1



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