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Vector Algebra

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  1. 201.Let a= i+3 j- k, b=3 i- j+4 k, c= i+2 j-2 k.
  2. 202.A,B,C have position vectors a= i+4 j+3 k, b=2 i+ j+4 k, c=3 i-2 j+5 k.
  3. 203.Let a= i-2 j+3 k, b= i+ j+ k, and c satisfy a+( b c)= 0 and b c=5.
  4. 204.Let a, b be unit vectors, angle between a and c is 12, and b= c+2( c a).
  5. 205.If the shortest distance between the lines r=- i+3 k+( i-a j) and r=- j+2 k+( i- j+ k) is …
  6. 206.Let ABC be a triangle with BC= a, CA= b, AB= c, | a|=6√2, | b|=2√3, b c=12.
  7. 207.Let a= i- j+2 k, and b satisfy a b=2 i- k, a b=3.
  8. 208.Let a= i+ j- k, b=2 i+ j- k, >0.
  9. 209.Let a= i+ j+ k, b=3 i-5 j+4 k, with a b=- i+9 j+12 k.
  10. 210.Let a=2 i- j+5 k, b= i+ j+2 k.
  11. 211.Let a, b, c be non-coplanar vectors with a b=4 c, b c=9 a, c a= b (>0).
  12. 212.Let a=(1+t) i+(1-t) j+ k, b=(1-t) i+(1+t) j+2 k, c=t i-t j+ k, t R, be such that a+ b+ c= …
  13. 213.Let a have magnitude 9.
  14. 214.Let S be the set of a R for which the angle between u=a( b) i-6 j+3 k and v=( b) i+2 j+2a(…
  15. 215.Let a=3 i+ j, b= i+2 j+ k.
  16. 216.Let a, b be unit vectors with angle 4 between them.
  17. 217.If (2,3,9), (5,2,1), (1,,8), (,2,3) are coplanar, the product of all possible values of is…
  18. 218.Let a, b, c be coplanar, concurrent vectors with equal pairwise angles.
  19. 219.Let a, b satisfy | a+ b|^2=| a|^2+2| b|^2, a b=3, | a b|^2=75.
  20. 220.If (1,5,35), (7,5,5), (1,,7), (2,1,2) are coplanar, the sum of all possible values of is:
  21. 221.If a and b are perpendicular, then a( a( a( a b))) is equal to:
  22. 222.Let a, b, c be such that c is coplanar with a, b, a c=7, b c, where a=- i+ j+ k, b=2 i+ k.
  23. 223.If a_1=x i- j+ k and a_2= i+y j+z k are collinear, a possible unit vector parallel to x i+…
  24. 224.Let a= i+ j+3 k, b=3 i- j+ k.
  25. 225.Let a= i+2 j- k, b= i- j, c= i- j- k.
  26. 226.A vector a has components 3p,1 in a rectangular system.
  27. 227.A vector i+ j is obtained by rotating √3 i+ j by 45^ counterclockwise.
  28. 228.Let x lie in the plane of a=2 i- j+ k and b= i+2 j- k.
  29. 229.Let a, b be non-zero, perpendicular, | a|=| b|, and | a b|=| a|.
  30. 230.Let a=2 i-3 j+4 k, b=7 i+ j-6 k.
  31. 231.Let a= i+2 j-3 k, b=2 i-3 j+5 k.
  32. 232.Let c be perpendicular to a= i+ j- k and b= i+2 j+ k.
  33. 233.Let a= i+ j+3 k, b=- i- j- k, c= i-2 j- k, with a b=1 and b c=-3.
  34. 234.Let O be the origin, OP=x i+y j- k, OQ=- i+2 j+3x k (x,y R,x>0), with |PQ|=√20 and OPOQ.
  35. 235.If ( a+3 b)(7 a-5 b) and ( a-4 b)(7 a-2 b), then the angle between a and b (in degrees) is…
  36. 236.Let a, b, c be mutually perpendicular vectors of equal magnitude, equally inclined at angl…
  37. 237.For p>0, v_2=2 i+(p+1) j is obtained by rotating v_1=√3p i+ j by angle counterclockwise.
  38. 238.In ABC, |BC|=3, |CA|=5, |BA|=7.
  39. 239.Let p=2 i+3 j+ k, q= i+2 j+ k.
  40. 240.If | a|=2, | b|=5, | a b|=8, then a b is:
  41. 241.Let a= i+ j+2 k, b=- i+2 j+3 k.
  42. 242.Let a= i+ j+ k, c= j- k, and b satisfy a b= c, a b=1.
  43. 243.Let a, b, c satisfy a= b( b c), with | a|=√2,| b|=1,| c|=2, and angle (0,2) between b, c.
  44. 244.If (2+a+b) i+(a+2b+c) j-(b+c) k, (1+b) i+2b j-b k, (2+b) i+2b j+(1-b) k are coplanar, whic…
  45. 245.Let a, b, c satisfy a b= c, b c= a, | a|=2.
  46. 246.Let a be coplanar with b=2 i+ j+ k, c= i- j+ k, perpendicular to d=3 i+2 j+6 k, with | a|=…
  47. 247.Let a=2 i+ j-2 k, b= i+ j.
  48. 248.Let a, b satisfy |2 a+3 b|=|3 a+ b|, angle between them 60^.
  49. 249.Let a, b, c be mutually perpendicular, equal magnitude.
  50. 250.A hall has a 10 m10 m square floor and vertical walls.