Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Manipal MET2014MathematicsVector Algebra

If | a |=1,| b |=4, a b =2 and c =2 a b -3 b , then the angle between b and c is

Options

  1. A6
  2. B5 6
  3. C3
  4. D2 2

Correct answer

B. 5 6

Step-by-step solution

aligned & | a b |^2=|a|^2| b |^2-2( a b )^2=16-4=12 and & aligned |c|^2=(2 a b -3 b )^2 & =(2 a b -3 b ) & =4| a b |^2+9| b |^2=4.12+9.16 & =192 | c |=8 3 aligned aligned Now, b c = b (2 a b -3 b )=-3| b |^2=-48 aligned & & & = b c |b||c| =- 48 4 8 3 =- 3 2 & & & = 5 6 aligned

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 Manipal MET PYQs