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Vector Algebra

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  1. 301.If | a|=2, | b|=3 and |2 a- b|=5, then |2 a+ b| equals:
  2. 302.If [( a b) ( b c) ( c a)]=[ a b c]^2, then is equal to:
  3. 303.If x=3 i-6 j- k, y= i+4 j-3 k and z=3 i-4 j-12 k, then the magnitude of the projection of …
  4. 304.If | c|^2=60 and c( i+2 j+5 k)= 0, then a value of c(-7 i+2 j+3 k) is:
  5. 305.If the vectors AB=3 i+4 k and AC=5 i-2 j+4 k are the sides of a triangle ABC, then the len…
  6. 306.If a and b are non-collinear vectors, then the value of for which the vectors u=(-2) a+ b …
  7. 307.If a, b and c are unit vectors satisfying a-√3 b+ c= 0, then the angle between the vectors…
  8. 308.Let a=2 i- j+ k, b= i+2 j- k and c= i+ j-2 k be three vectors.
  9. 309.Let a=2 i+ j-2 k, b= i+ j.
  10. 310.The vector ( i( a b)) i+( j( a b)) j+( k( a b)) k is equal to:
  11. 311.Statement 1: If the points (1,2,2), (2,1,2), (2,2,z) and (1,1,1) are coplanar, then z=2.
  12. 312.If a= i-2 j+3 k, b=2 i+3 j- k and c=r i+ j+(2r-1) k are three vectors such that c is paral…
  13. 313.Let ABCD be a parallelogram such that AB= q, AD= p and BAD be an acute angle.
  14. 314.Let a and b be two unit vectors.
  15. 315.If a+ b+ c= 0, | a|=3, | b|=5 and | c|=7, then the angle between a and b is:
  16. 316.A unit vector which is perpendicular to the vector 2 i- j+2 k and is coplanar with the vec…
  17. 317.ABCD is a parallelogram.
  18. 318.Statement 1: The vectors a, b and c lie in the same plane if and only if a( b c)=0.
  19. 319.If u= j+4 k, v= i+3 k and w=, i+, j are vectors in 3-dimensional space, then the maximum p…
  20. 320.If a= i-2 j+3 k, b=2 i+3 j- k and c= i+ j+(2-1) k are coplanar vectors, then is equal to:
  21. 321.Let a, b, c be three non-zero vectors which are pairwise non-collinear.
  22. 322.If the vectors p i+ j+ k, i+q j+ k and i+ j+r k (p q r 1) are coplanar, then the value of …
  23. 323.The vectors a and b are not perpendicular, and c and d are two vectors satisfying b c= b d…
  24. 324.If a=1√10(3 i+ k) and b=17(2 i+3 j-6 k), then the value of (2 a- b)[( a b)( a+2 b)] is:
  25. 325.If the vectors a= i- j+2 k, b=2 i+4 j+ k and c= i+ j+ k are mutually orthogonal, then (,)=
  26. 326.Let a= j- k and c= i- j- k.
  27. 327.If u, v, w are non-coplanar vectors and p,q are real numbers, then the equality [3 u p v p…
  28. 328.The vector a= i+2 j+ k lies in the plane of the vectors b= i+ j and c= j+ k and bisects th…
  29. 329.The non-zero vectors a, b and c are related by a=8 b and c=-7 b.
  30. 330.Let a= i+ j+ k, b= i- j+2 k and c=x i+(x-2) j- k.
  31. 331.If u and v are unit vectors and is the acute angle between them, then 2 u3 v is a unit vec…
  32. 332.A particle just clears a wall of height b at a distance a and strikes the ground at a dist…
  33. 333.A body weighing 13 kg is suspended by two strings 5 m and 12 m long, their other ends bein…
  34. 334.The resultant of two forces P N and 3 N is a force of 7 N.
  35. 335.ABC is a triangle, right angled at A.
  36. 336.The values of a, for which points A,B,C with position vectors 2 i- j+ k, i-3 j-5 k and a i…
  37. 337.If ( a b) c= a( b c) where a, b and c are any three vectors such that a b0, b c0, then a a…
  38. 338.A body falling from rest under gravity passes a certain point P.
  39. 339.A particle has two velocities of equal magnitude inclined to each other at an angle .
  40. 340.If C is the mid point of AB and P is any point outside AB, then:
  41. 341.Let a,b,c be distinct non-negative numbers.
  42. 342.Let a= i- k, b=x i+ j+(1-x) k and c=y i+x j+(1+x-y) k.
  43. 343.If a, b, c are non-coplanar vectors and is a real number, then [( a+ b) ^2 b c]=[ a b+ c b…
  44. 344.For any vector a, the value of | a i|^2+| a j|^2+| a k|^2 is equal to:
  45. 345.The resultant R of two forces acting on a particle is at right angles to one of them, and …
  46. 346.A and B are two like parallel forces.
  47. 347.A particle is projected from a point O with velocity u at an angle of 60^ with the horizon…
  48. 348.If a, b, c are non-coplanar vectors and is a real number, then the vectors a+2 b+3 c, b+4 …
  49. 349.Let a, b and c be three non-zero vectors such that no two of these are collinear.
  50. 350.Let u, v, w be such that | u|=1,| v|=2,| w|=3.