Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
COMEDK2022MathematicsVector Algebra

If x, y and z are non-zero real numbers and a =x i +2 j , b = y j +3 k and c =x i +y j +z k are such that a b =z i -3 j + k , then [ a b c ] is equal to

Options

  1. A3
  2. B10
  3. C9
  4. D6

Correct answer

C. 9

Step-by-step solution

Given vectors a = x i + 2 j , b = y j + 3 k , and c = x i + y j + z k . Calculate the cross product a b : a b = vmatrix i & j & k x & 2 & 0 0 & y & 3 vmatrix = i (6 - 0) - j (3x - 0) + k (xy - 0) = 6 i - 3x j + xy k . Given a b = z i - 3 j + k , compare the components: z = 6 , -3x = -3 x = 1 , and xy = 1 . Since x = 1 and xy = 1 , we get y = 1 . The scalar triple product [ a b c ] is defined as ( a b ) c . [ a b c ] = (z i - 3 j + k ) (x i + y j + z k ) . Substitute the values x=1, y=1, z=6 : [ a b c ] = (6 i - 3 j

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 COMEDK PYQs