Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202616 April 2026Morning ShiftMathematicsVector AlgebraActual

Let A, B, C, D be the points in the plane with position vectors -2 i - j , 4 i , 3 i + 3 j and -3 i + 2 j respectively, then ABCD is

Options

  1. Aa parallelogram which is neither a rhombus nor a reactangle
  2. Ba square
  3. Ca rectangle but not a square
  4. Da rhombus but not a square

Correct answer

A. a parallelogram which is neither a rhombus nor a reactangle

Step-by-step solution

The position vectors of the vertices are given as A = -2 i - j , B = 4 i , C = 3 i + 3 j , and D = -3 i + 2 j . The vectors representing the sides of the quadrilateral are: AB = B - A = (4 - (-2)) i + (0 - (-1)) j = 6 i + j BC = C - B = (3 - 4) i + (3 - 0) j = - i + 3 j CD = D - C = (-3 - 3) i + (2 - 3) j = -6 i - j DA = A - D = (-2 - (-3)) i + (-1 - 2) j = i - 3 j Since AB = - CD and BC = - DA , the opposite sides are equal and parallel. Thus, ABCD is a parallelogram. The lengths of adjacent sides are: | AB | = 6^

Practice Vector Algebra on Quantrex Academy →

More from Vector Algebra

P is the circumcentre of A B C . If the position vectors of A, B, C and P are a , b , c , a + b + c 4 respectively, then the position vector of the orthocentre of this triangle is 2025If the position vectors of A, B, C, D are i +2 j +2 k , 2 i - j , i + j +3 k and 4 j +5 k respectively, then the quadrilateral ABCD is a 2025The set of all real values of c so that the angle between the vectors a = cx i -6 j +3 k and b =x i +2 j +2 cx k is an obtuse angle for all real x is 2025Let a =2 i + j +3 k , b =3 i +3 j + k and c = i -2 j +3 k be three vectors. If r is a vector such that r a = r b and r c =18 , then the magnitude of the orthogonal projection of 4 2025If u , v , w are non coplanar vectors and p, q are real numbers, then the equality [ array lll 3 u & p v & p w array ]- [ array lll p v & w & q u array ]- [ array lll 2 w & q v & q 2025Let i -2 j + k , i + j -2 k , 2 i - j - k and i + j + k be the position vectors of four points A , B , C and D respectively. If a point P divides AB in the ratio 2: 1 internally an 2025If a = i + j , b =2 j - k are two vectors such that r a = b a , r b = a b , then the unit vector in the direction of r is 2025If a , b , c are three unit vectors such that a ( b c )= 3 2 b + c 2 and , are the angles between a , c and a , b respectively, then + = 2025 Full Vector Algebra list All MHT CET PYQs