Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202526 Apr 2025Evening ShiftMathematicsVector AlgebraActual

If a , ~b , c are three coplanar vectors such that | a |=1,| ~b |=2, ~b c =8 and the angle between b and c is 45^ then the value of | a ( b c )| is

Options

  1. A8
  2. B2
  3. C2
  4. D5

Correct answer

A. 8

Step-by-step solution

Given vectors a , b , and c are coplanar with magnitudes | a | = 1 and | b | = 2 , and b c = 8 at a 45^ angle. The magnitude of c is determined using the dot product: 8 = 2| c | 45^ , so 8 = 2| c | 1 2 = 2 | c | , yielding | c | = 8 2 = 4 2 . The magnitude of the cross product is then | b c | = 2 4 2 45^ = 8 2 1 2 = 8 . Since a is coplanar with b and c , it is perpendicular to b c , which is normal to their plane. Thus, the angle between a and b c is 90^ , and | a ( b c )| = | a || b c | 90^ = 1 8 1 = 8 . Answer: 8

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