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Vector Algebra

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  1. 251.If the projection of i+2 j+ k on the sum of 2 i+4 j-5 k and - i+2 j+3 k is 1, then is ____…
  2. 252.Let a= i+5 j+ k, b= i+3 j+ k, c=- i+2 j-3 k, with | b c|=5√3 and a b.
  3. 253.If _r=1^50^-1(12r^2)=p, then p is:
  4. 254.Let a= i+ j+ k, b= j- k.
  5. 255.Let P_1,,P_15 be 15 points on a circle.
  6. 256.A vector a= i+2 j+ k lies in the plane of b= i+ j, c= i- j+4 k.
  7. 257.Let a, b, c be unit vectors with a+ b+ c= 0.
  8. 258.Let the volume of a parallelepiped with coterminous edges u= i+ j+ k, v= i+ j+3 k, w=2 i+ …
  9. 259.Let a= i-2 j+ k, b= i- j+ k.
  10. 260.The projection of the segment joining (1,-1,3) and (2,-4,11) on the line joining (-1,2,3) …
  11. 261.Let a, b, c satisfy | a|=√3, | b|=5, b c=10, angle between b, c is 3, and a( b c).
  12. 262.Let a, b, c satisfy | a|=2, | b|=4, | c|=4.
  13. 263.If p=(a+1) i+a j+a k, q=a i+(a+1) j+a k, r=a i+a j+(a+1) k (a R) are coplanar, and 3( p q)…
  14. 264.Let a,b,c R with a^2+b^2+c^2=1.
  15. 265.Let A=(1,1,1), B=(2,1,3) (position vectors), and P divide AB internally in ratio :1 (>0).
  16. 266.If a, b are unit vectors, the greatest value of √3| a+ b|+| a- b| is _______.
  17. 267.If x, y are non-zero vectors with | x+ y|=| x|, and 2 x+ y is perpendicular to y, then is …
  18. 268.Let a, b, c be unit vectors with | a- b|^2+| a- c|^2=8.
  19. 269.If the volume of a parallelepiped with edges a= i+ j+n k, b=2 i+4 j-n k, c= i+n j+3 k (n0)…
  20. 270.Let x_0 be the point of local maxima of f(x)= a( b c), where a=x i-2 j+3 k, b=-2 i+x j- k,…
  21. 271.If a=2 i+ j+2 k, then | i( a i)|^2+| j( a j)|^2+| k( a k)|^2 equals ________.
  22. 272.The sum of the distinct real values of for which i+ j+ k, i+ j+ k, i+ j+ k are coplanar is…
  23. 273.Let a= i+2 j+4 k, b= i+ j+4 k, c=2 i+4 j+(^2-1) k be coplanar.
  24. 274.Let √3 i+ j, i+√3 j, i+(1-) j be position vectors of A,B,C.
  25. 275.Let =(-2) a+ b and =(4-2) a+3 b ( a, b non-collinear).
  26. 276.Let a=2 i+_1 j+3 k, b=4 i+(3-_2) j+6 k, c=3 i+6 j+(_3-1) k, with b=2 a and a c.
  27. 277.Let a= i+ j+√2 k, b=b_1 i+b_2 j+√2 k, c=5 i+ j+√2 k, with the projection vector of b on a …
  28. 278.Let a, b, c be unit vectors, b, c non-parallel.
  29. 279.Let a= i- j, b= i+ j+ k, and c satisfy a c+ b= 0, a c=4.
  30. 280.Let a=3 i+2 j+2 k, b= i+2 j-2 k.
  31. 281.If the volume of the parallelepiped formed by i+ j+ k, j+ k, i+ k is minimum, then is:
  32. 282.Let R and a= i+ j+3 k, b=2 i+ j- k, c= i-2 j+3 k.
  33. 283.If a unit vector a makes angles 3 with i, 4 with j, and (0,) with k, a value of is:
  34. 284.Let =3 i+ j, =2 i- j+3 k.
  35. 285.The magnitude of the projection of 2 i+3 j+ k on the vector perpendicular to the plane con…
  36. 286.Let a=3 i+2 j+x k, b= i- j+ k.
  37. 287.Let u be coplanar with a=2 i+3 j- k, b= j+ k.
  38. 288.The position vectors of A,B,C of ABC are 4 i+7 j+8 k, 2 i+3 j+4 k, 2 i+5 j+7 k.
  39. 289.Let a= i+ j+ k, c= j- k, and b satisfy a b= c, a b=3.
  40. 290.If a, b, c are unit vectors with a+2 b+2 c= 0, then | a c| is:
  41. 291.Let a=2 i+ j-2 k and b= i+ j.
  42. 292.If the vector b=3 j+4 k is written as the sum of a vector b_1, parallel to a= i+ j, and a …
  43. 293.The area (in sq.
  44. 294.Let ABC be a triangle whose circumcentre is at P.
  45. 295.In a triangle ABC, right angled at the vertex A, if the position vectors of A, B and C are…
  46. 296.Let a, b and c be three unit vectors such that a( b c)=√32( b+ c).
  47. 297.Let a, b and c be three non-zero vectors such that no two of them are collinear and a( b c…
  48. 298.In a parallelogram ABCD, AB=a, AD=b and AC=c, then DAAB has the value:
  49. 299.Let a and b be two unit vectors such that | a+ b|=√3.
  50. 300.If x, y and z are three unit vectors in three-dimensional space, then the minimum value of…