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Vector Algebra

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  1. 51.Consider three vectors a,b,c.
  2. 52.If A(1,-1,2),B(5,7,-6),C(3,4,-10) and D(-1,-4,-2) are the vertices of a quadrilateral ABCD…
  3. 53.For >0, let be the angle between the vectors a=i+ j-3k and b=3i-j+2k.
  4. 54.Let a=i+j+k,b=2i+4j-5k and c=xi+2j+3k,x R.
  5. 55.Let a unit vector which makes an angle of 60^ with 2i+2j-k and an angle of 45^ with i-k be…
  6. 56.Let a=-5i+j-3k, b=i+2j-4k and c=((( a b) i) i) i.
  7. 57.Let a=3i+j-2k,b=4i+j+7k and c=i-3j+4k be three vectors.
  8. 58.The distance of the point Q(0,2,-2) form the line passing through the point P(5,-4, 3) and…
  9. 59.Let a=i+ j+ k, , R.
  10. 60.Let a and b be two vectors such that |b|=1 and |b a|=2.
  11. 61.Let a=a_1i+a_2j+a_3k and b=b_1i+b_2j+b_3k be two vectors such that | a|=1,a b=2 and |b|=4.
  12. 62.Let a unit vector u=xi+yj+zk make angles ( )/(2),( )/(3) and (2 )/(3) with the vectors 1√2…
  13. 63.Let OA=a, OB=12a+4b OC=b, where O is the origin.
  14. 64.Let a,b and c be three non-zero vectors such that b and c are non-collinear.
  15. 65.Let the position vectors of the vertices A,B and C of a triangle be 2i+2j+k,i+2j+2k and 2i…
  16. 66.The position vectors of the vertices A,B and C of a triangle are 2i-3j+3k,2i+2j+3k and -i+…
  17. 67.Let a=i+2j+k, b=3(i-j+k).
  18. 68.Let S be the set of all ( , ) for which the vectors i-j+k,i+2j+ k and 3i-4j+5k, where - =5…
  19. 69.Let ABCD be a quadrilateral.
  20. 70.Let |a|=2,|b|=3 and the angle between the vectors a and b be ( )/(4).
  21. 71.Let for a triangle ABC, AB=-2i+j+3k CB= i+ j+ k CA=4i+3j+ k If >0 and the area of the tria…
  22. 72.Let a=i+4j+2k,b=3i-2j+7k and c=2i-j+4k.
  23. 73.Let a,b,c be three distinct real numbers, none equal to one.
  24. 74.Let Z,a= i+j-k and b=3i-j+2k.
  25. 75.If four distinct points with position vectors a,b,c and d are coplanar, then [a, , b, , c]…
  26. 76.For any vector a=a_1i+a_2j+a_3k, with 10|a_i|(A): max|a_1|,|a_2|,|a_3| |a| (B) :
  27. 77.Let a be a non-zero vector parallel to the line of intersection of the two planes describe…
  28. 78.Let a=2i+7j-k,b=3i+5k and c=i-j+2k.
  29. 79.If the points P and Q are respectively the circumcenter and the orthocentre of a , then PA…
  30. 80.Let O be the origin and the position vector of the point P be -i-2j+3k.
  31. 81.An arc PQ of a circle subtends a right angle at its centre O.
  32. 82.Let the vectors u_1=i+j+ak,u_2=i+bj+k and u_3=ci+j+k be coplanar.
  33. 83.The area of the quadrilateral ABCD with vertices A(2,1,1),B(1,2,5),C(-2,-3,5) and D(1,-6,-…
  34. 84.If the points with position vectors i+10j+13k,6i+11j+11k,(9)/(2)i+ j-8k are collinear, the…
  35. 85.Let the vectors a,b,c represent three coterminous edges of a parallelopiped of volume V.
  36. 86.The sum of all values of , for which the points whose position vectors are i-2j+3k,2i-3j+4…
  37. 87.Let the position vectors of the points A, B, C and D be 5i+5j+2 k,i+2j+3k,-2i+ j+4k and -i…
  38. 88.Let a=2i+3j+4k,b=i-2j-2k and c=-i+4j+3k.
  39. 89.Let a=i+2j+3k,b=i-j+2k and c=5i-3j+3k be three vectors.
  40. 90.Let R,a= i+2j-3k,b=i- j+2k.
  41. 91.Let a and b be two vectors, Let |a|=1,|b|=4 and a b=2.
  42. 92.Let a, b, c be three non-zero vectors which are pairwise non-collinear.
  43. 93.If a=i+j+k,b=j-k and c be three vectors such that a c=b and a c=3, then c (a-2b) is equal …
  44. 94.If the distance of the point P(43, , ), <0, from the line r=4i-k+ (2i+3k), R along a line …
  45. 95.Let PQR be a triangle such that PQ=-2i-j+2k and PR=ai+bj-4k,a,b Z.
  46. 96.Let a vector a=√2i-j+ k, >0, make an obtuse angle with the vector b=- ^2i+4√2j+4√2k and an…
  47. 97.Let the three sides of a triangle ABC be given by the vectors 2i-j+k,i-3j-5k and 3i-4j-4k.
  48. 98.Let a=i+2j+k,b=3i-3j+3k,c=2i-j+2k and d be a vector such that b d=c d and a d=4.
  49. 99.Let a=i+j+k,b=3i+2j-k,c= j+ k and d be a unit vector such that a d=b d and c d=1.
  50. 100.Let a=i+j+k, b=2i+2j+k and d=a b.