Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202617 April 2026Evening ShiftMathematicsVector AlgebraActual

Let a = i + j + k , b = 2 i + 4 j + 4 k , c = i + j + k If a is parallel to b and b is perpendicular to c then - =

Options

  1. A-2
  2. B-1
  3. C2
  4. D1

Correct answer

C. 2

Step-by-step solution

Given a = i + j + k and b = 2 i + 4 j + 4 k . Since a is parallel to b , their corresponding components are proportional: 2 = 1 4 = 1 4 = 1 2 Given c = i + j + k . Since b is perpendicular to c , their dot product is zero: b c = 0 (2)(1) + (4)( ) + (4)(1) = 0 2 + 4 + 4 = 0 4 = -6 = - 3 2 Calculating - : - = 1 2 - (- 3 2 ) = 1 2 + 3 2 = 2 Answer: 2

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