Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET201824 Apr 2018Morning ShiftMathematicsVector AlgebraActual

If a , b , c are three non-coplanar vectors, then match the items of List-I with those of List-II. The correct answer is A B B D

Options

  1. AIII IV V II
  2. BIV V II III
  3. CI IV V III
  4. DI IV II III

Correct answer

D. I IV II III

Step-by-step solution

aligned & (A) [ b c c a a b ] & =( b c ) ( c a ) ( a b ) & = d ( c a ) ( a b ) & = ( d a ) c -( d c ) a ( a b ) & = [ a b c ] c -[ b c c a ( a b ) & = [ a b c c -0 ( a b ) & =[ a b c ] c ( a b ) & =[ a b c ][ c a b ] & =[ a b c ]^2 aligned (B) aligned & [ a b a c b ] & = ( a b ) ( a c ) b & = d ( a c ) b [ let d = a b ] & = ( d c ) a -( d a ) c b & = ( a b ) c a b - ( a b ) a c b & =[ a b c ][ a b ]-[ a b a ][ c b ] & =[ a b c ][ a b ]-0 & =[ a b c ][ a b ] aligned (C) aligned & [ a + b b + c c + a ] & =( a + b ) (

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 AP EAMCET PYQs