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Vector Algebra

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  1. 101.Let c be the projection vector of b= i+4k, >0, on the vector a=i+2j+2k.
  2. 102.Let a=9i-13j+25k,b=3i+7j-13k and c=17i-2j+k be three given vectors.
  3. 103.Let a=2i-3j+4k,b=3i+4j-5k and a vector c be such that a (b+c)+b c=i+8j+13k.
  4. 104.Let a=i-3j+7k, b=2i-j+k and c be a vector such that ( a+2 b) c=3( c a).
  5. 105.Let ABC be a triangle of area 15√2 and the vectors AB=i+2j-7k, BC=ai+bj+ck and AC=6i+dj-2k…
  6. 106.Let a=i+j+k, b=-i-8j+2k and c=4i+c_2j+c_3k be three vectors such that b a= c a.
  7. 107.Let a=3i+2j+k,b=2i-j+3k and c be a vector such that (a+b) c=2(a b)+24j-6k and (a-b+i) c=-3…
  8. 108.Let a and b be two vectors such that |a|=1,|b|=4, and a b=2.
  9. 109.The least positive integral value of , for which the angle between the vectors i-2j+2k and…
  10. 110.Let a=3i+j-k and c=2i-3j+3k.
  11. 111.Let a=i+2j+3k and b=i+j-k.
  12. 112.Let a=6i+9j+12k,b= i+11j-2k and c be vectors such that a c=a b.
  13. 113.Let a,b,c be three vectors such that |a|=√31,4|b|=|c|=2 and 2(a b)=3(c a).
  14. 114.In PQR, PQ = -2 i - j + 2 k and PR = a i + b j - 4 k, a,b Z, with |PR| = 9.
  15. 115.Let a = √2 i - j + k, >0 and b = -^2 i + 4√2 j + 4√2 k.
  16. 116.A point P(43,,), <0, has its distance from the line r = 4 i - k + (2 i+3 k), R, measured a…
  17. 117.Let c and d be vectors such that | c+ d| = √29 and c (2 i+3 j+4 k) = (2 i+3 j+4 k) d.
  18. 118.Let (,,) be the coordinates of the foot of the perpendicular drawn from the point (5,4,2) …
  19. 119.Let AB = 2 i+4 j-5 k and AD = i+2 j+ k, R, be adjacent sides of a parallelogram ABCD.
  20. 120.Let a = i-2 j+3 k, b = 2 i+ j- k, c = i+ j+ k, and v = a b.
  21. 121.Let the lines L_1: r = i+2 j+3 k+(2 i+3 j+4 k) and L_2: r = (4 i+ j)+(5 i+2 j+ k) intersec…
  22. 122.Let a = 2 i- j- k, b = i+3 j- k, and c = 2 i+ j+3 k.
  23. 123.For three unit vectors a, b, c satisfying | a- b|^2+| b- c|^2+| c- a|^2 = 9 and |2 a+k b+k…
  24. 124.If a and b are two vectors such that | a|=2, | b|=3, and a b=6, then the maximum value of …
  25. 125.Let a = √7 i+ j- k and b= j+2 k.
  26. 126.Let O be the origin, OP= a and OQ= b.
  27. 127.Let the three sides of triangle ABC be given by the vectors 2 i- j+ k (=AB), i-3 j-5 k (=B…
  28. 128.An arc AC of a circle subtends a right angle at the centre O.
  29. 129.The position vectors of vertices A,B,C of a tetrahedron ABCD are i+2 j+ k, i+3 j-2 k, 2 i+…
  30. 130.Let point A divide the line segment joining P(-1,-1,2) and Q(5,5,10) internally in the rat…
  31. 131.Let a= i+2 j+3 k, b=3 i+ j- k, and c be a vector coplanar with a and b.
  32. 132.Let a=3 i- j+2 k, b = a( i-2 k), c = b k.
  33. 133.Let the position vectors of the vertices of a triangle be such that the orthocenter is p+ …
  34. 134.Let A,B,C be points in the xy-plane with position vectors OA=√3 i+ j, OB= i+√3 j, OC=a i+(…
  35. 135.If the components of a= i+ j+ k along and perpendicular to b=3 i+ j- k are 1611(3 i+ j- k)…
  36. 136.Let a= i+2 j+ k, b=2 i+7 j+3 k.
  37. 137.Let a be a unit vector perpendicular to the vectors i-2 j+3 k and 2 i+3 j- k, making an an…
  38. 138.If a is a nonzero vector such that its projections on the vectors 2 i- j+2 k, i+2 j-2 k, a…
  39. 139.Let the angle between two unit vectors a and b (0<<2) be ^-1(√659).
  40. 140.Let a = i+2 j+ k and b = 2 i+ j- k.
  41. 141.Let a = i+2 j+ k, b = 3 i- j+ k.
  42. 142.Let OA= a, OB=12 a+4 b, OC= b, where O is the origin.
  43. 143.Let a unit vector u = x i+y j+z k make angles 2, 3, 23 with the vectors 1√2 i+1√2 k, 1√2 j…
  44. 144.Let A(2,3,5) and C(-3,4,-2) be opposite vertices of a parallelogram ABCD.
  45. 145.Let a = i+ j+ k, , R.
  46. 146.Let a = 3 i+ j-2 k, b = 4 i+ j+7 k, and c = i-3 j+4 k.
  47. 147.Consider ABC where A(1,2,3), B(-2,8,0) and C(3,6,7).
  48. 148.Let a= i+ j+ k, b=- i-8 j+2 k, and c=4 i+c_2 j+c_3 k be vectors such that b a= c a.
  49. 149.Let a, b, c be non-zero, non-coplanar vectors.
  50. 150.Let u= i- j-2 k, v=2 i+ j- k, v w=2, and v w= u+ v.