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Vector Algebra

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  1. 151.Let =4 i+3 j+5 k and = i+2 j-4 k.
  2. 152.Let a= i+2 j+ k, b=3 i-5 j- k, with a c=7, b c=-432, and a c= b c.
  3. 153.The vector a=- i+2 j+ k is rotated through a right angle, passing through the y-axis in it…
  4. 154.Let a, b, c be non-zero vectors with b c=0 and a( b c) = b- c2.
  5. 155.If the points with position vectors 3 i-4 j+2 k, i+2 j- k, -2 i- j+3 k, 5 i-2 j+4 k are co…
  6. 156.Let a=- i- j+ k, a b=1, and a b= i- j.
  7. 157.If a= i+ j+4 k, b=-2 i+4 j-2 k, and c=2 i+3 j+ k are coplanar, and the projection of a on …
  8. 158.Let a=4 i+3 j and b=3 i-4 j+5 k, and c be a vector such that c( a b)+25=0, c( i+ j+ k)=4, …
  9. 159.If a= i+2 k, b= i+ j+ k, c=7 i-3 j+4 k, r b= c b, and r a=0, then r c is equal to:
  10. 160.If a, b, c are non-zero vectors and n is a unit vector perpendicular to c such that a= b- …
  11. 161.Let R, a= i+2 j-3 k, b= i- j+2 k.
  12. 162.Let a and b be two vectors such that | a|=1, | b|=4, and a b=2.
  13. 163.Let a=2 i+ j+ k, and b, c be non-zero vectors such that | a+ b+ c|=| a+ b- c| and b c=0.
  14. 164.Let a, b be vectors with | a|=√14, | b|=√6, | a b|=√48.
  15. 165.Let a= i+2 j+3 k, b= i- j+2 k, c=5 i-3 j+3 k.
  16. 166.The foot of the perpendicular from the origin O to a plane P, which meets the coordinate a…
  17. 167.Let a, b, c be vectors such that | a|=√31, | b|=1, | c|=2, and 2( a b)=3( c a).
  18. 168.Let v= i+2 j-3 k, w=2 i+ j- k, and u be a vector with | u|=>0.
  19. 169.A(2,6,2), B(-4,0,), C(2,3,-1), D(4,5,0), ||5, are vertices of quadrilateral ABCD.
  20. 170.Let a=5 i- j-3 k and b= i-3 j+5 k.
  21. 171.Let a=2 i-7 j+5 k, b= i+ k, c= i+2 j-3 k.
  22. 172.Let the position vectors of A,B,C,D be 5 i+5 j+2 k, i+2 j+3 k, -2 i+ j+4 k, - i+5 j+6 k.
  23. 173.Let a=2 i+3 j+4 k, b= i-2 j-2 k, c=- i+4 j+3 k.
  24. 174.Let a, b, c be coterminous edges of a parallelepiped of volume V.
  25. 175.The sum of all values of for which the points with position vectors i-2 j+3 k, 2 i-3 j+4 k…
  26. 176.Let a=6 i+9 j+12 k, b= i+11 j-2 k, and c satisfy a( c- b)= 0.
  27. 177.Let u_1= i+ j+a k, u_2= i+b j+ k, u_3=c i+ j+ k be coplanar.
  28. 178.An arc PQ of a circle subtends a right angle at its centre O.
  29. 179.Let a=2 i+7 j- k, b=3 i+5 k, c= i- j+2 k.
  30. 180.For a=a_1 i+a_2 j+a_3 k, consider: (A) |a_1|,|a_2|,|a_3|| a| (B) | a|√3|a_1|,|a_2|,|a_3|
  31. 181.Let a be a non-zero vector parallel to the line of intersection of the planes normal to i+…
  32. 182.If four distinct points with position vectors a, b, c, d are coplanar, then [ a b c] equal…
  33. 183.Let a= i+2 j+3 k, b= i+ j- k.
  34. 184.Let a,b,c be three distinct reals, none equal to 1.
  35. 185.Let Z, a= i+ j- k, b=3 i- j+2 k.
  36. 186.Let a=3 i+ j- k, c=2 i-3 j+3 k.
  37. 187.Let a= i+4 j+2 k, b=3 i-2 j+7 k, c=2 i- j+4 k.
  38. 188.Let | a|=2, | b|=3, angle between them 4.
  39. 189.Let S be the set of (,) for which i- j+ k, i+2 j+ k, 3 i-4 j+5 k (with -=5) are coplanar.
  40. 190.Let ABCD be a quadrilateral.
  41. 191.Let a and b be two unit vectors such that | a+ b+2( a b)|=2.
  42. 192.Let be the angle between a, b where | a|=4, | b|=3, (4,3).
  43. 193.Let b= i+ j+ k, R.
  44. 194.If a b=1, b c=2, c a=3, then a( b c)+ b( c a)+ c( a b) is equal to:
  45. 195.Let a= i+ j+2 k, b=2 i-3 j+ k, c= i- j+ k.
  46. 196.Let a= i+ j- k and c=2 i-3 j+2 k.
  47. 197.Let a, b be vectors along the diagonals of a parallelogram of area 2√2, angle between them…
  48. 198.If a=2 i+ j+3 k, b=3 i+3 j+ k, c=c_1 i+c_2 j+c_3 k are coplanar, a c=5, and b c, then 122(…
  49. 199.Let a= i+2 j- k, b=-2 i+ j+ k.
  50. 200.Let a(3 i+12 j+2 k).