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Vector Algebra

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  1. 1.Let a=4i-j+3k, b=10i+2j-k and a vector c be such that 2( a b)+3( b c)= 0.
  2. 2.Let a=2i+3j+3k and b=6i+3j+3k.
  3. 3.Let O be the origin, OP=a and OQ=b.
  4. 4.Let a=√7i+j-k and b=j+2k.
  5. 5.Let u and v be unit vectors inclined at an acute angle such that |u v|=√32.
  6. 6.Let the vectors a=-i+j+3k and b=i+3j+k.
  7. 7.Two adjacent sides of a parallelogram PQRS are given by PQ=j+k and PS=i-j.
  8. 8.If a and b are two vectors such that |a|=2 and |b|=3, then the maximum value of 3|(3a+2b)|…
  9. 9.Let P be a point in the plane of the vectors AB=3i+j-k and AC=i-j+3k such that P is equidi…
  10. 10.For three unit vectors a,b,c satisfying |a-b|^2+|b-c|^2+|c-a|^2=9|2a+kb+kc|=3 the positive…
  11. 11.Let a=2i-5j+5k and b=i-j+3k.
  12. 12.Let a=2i+j-2k,b=i+j and c=a b.
  13. 13.Let the lines L_1:r=i+2j+3k+ (2i+3j+4k), R and L_2:r=(4i+j)+ (5i+2j+k), R, intersect at th…
  14. 14.Let a,b,c be three vectors such that a b=2(a c).
  15. 15.Let a=i-2j+3k,b=2i+j-k,c= i+j+k and v=a b.
  16. 16.Let a=-i+j+2k, b=i-j-3k, c= a b and d= c a.
  17. 17.Let a=2i-j+k and b= j+2k, Z be two vectors.
  18. 18.Let AB=2i+4j-5k and AD=i+2j+ k, R.
  19. 19.For a triangle ABC, let p= BC,q= CA and r= BA.
  20. 20.Let a=-i+2j+2k, b=8i+7j-3k and c be a vector such that a c= b.
  21. 21.Let ( , , ) be the co-ordinates of the foot of the perpendicular drawn from the point (5,4…
  22. 22.Let c and d be vectors such that | c+ d|=√29 and c (2i+3j+4k)=(2i+3j+4k) d.
  23. 23.Let a=i+2j+k and b=2i+j-k.
  24. 24.Let a and b be the vectors of the same magnitude such that |a+b|+|a-b||a+b|-|a-b|=√2+1. Th…
  25. 25.Let the angle ,0< <( )/(2) between two unit vectors a and b be ^-1(√659).
  26. 26.Consider two vectors u=3i-j and v=2i+j- k, >0.
  27. 27.Let a=2i-3j+k,, b=3i+2j+5k and a vector c be such that (a-c) b=-18i-3j+12k and a c=3.
  28. 28.If a is a nonzero vector such that its projections on the vectors 2i-j+2k,i+2j-2k and k ar…
  29. 29.Let a be a unit vector perpendicular to the vectors b=i-2j+3k and c=2i+3j-k, and a makes a…
  30. 30.Let a=i+2j+k and b=2i+7j+3k.
  31. 31.Let a=2i-j+3k,b=3i-5j+k and c be a vector such that a c=a b=c b and (a+c) (b+c)=168.
  32. 32.If the components of a= i+ j+ k along and perpendicular to b=3i+j-k respectively, are (16)…
  33. 33.Let A, B, C be three points in xy-plane, whose position vector are given by √3 i+j, i+√3 j…
  34. 34.Let the position vectors of three vertices of a triangle be 4p+q-3r,-5p+q+2r and 2p-q+2r.
  35. 35.Let a=3i-j+2k, b= a (i-2k) and c= b k.
  36. 36.Let a=i+2j+3k,b=3i+j-k and c be three vectors such that c is coplanar with a and b.
  37. 37.Let the point A divide the line segment joining the points P(-1,-1,2) and Q(5,5,10) intern…
  38. 38.Let the position vectors of the vertices A,B and C of a tetrahedron ABCD be i+2j+k,i+3j-2k…
  39. 39.Let the arc A C of a circle subtend a right angle at the centre O.
  40. 40.Let a and b be two unit vectors such that the angle between them is ( )/(3).
  41. 41.Between the following two statements: Statement I : Let a=i+2j-3k and b=2i+j-k.
  42. 42.Let a=2i+ j+k,b=-i+k,c= j-k, where and are integers and =-6.
  43. 43.Let three vectors , a= i+4j+2k, b=5i+3j+4k, c=xi+yj+zk form a triangle such that c=a-b and…
  44. 44.Let OA=2a, OB=6a+5b and OC=3b, where O is the origin.
  45. 45.Let a=4i-j+k, b=11i-j+k and c be a vector such that ( a+ b) c= c (-2 a+3 b).
  46. 46.Let a=i+2j+3k, b=2i+3j-5k and c=3i-j+ k be three vectors.
  47. 47.The set of all , for which the vectors a= ti+6j-3k and b=ti-2j-2 tk are inclined at an obt…
  48. 48.Let a=2i+j-k,b=((a (i+j)) i) i.
  49. 49.Let a=6i+j-k and b=i+j.
  50. 50.Let a=2i+5j-k,b=2i-2j+2k and c be three vectors such that (c+i) (a+b+i)=a (c+i).