Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202020 Oct 2020Evening ShiftMathematicsVector AlgebraActual

If a , b , c are the position vectors of the points A (1,3,0), B (2,5,0), C (4,2,0) respectively and c =t₁ a +t₂ b , then value of t₁ t₂=

Options

  1. A-16
  2. B16
  3. C160
  4. D-160

Correct answer

D. -160

Step-by-step solution

From given conditions, wo war aligned 4 i +2 j &= t ₁( i +3 j )+ t ₂(2 i +5 j ) &= ( t ₁+2 t ₂ ) i + (3 t ₁+5 t ₂ ) j aligned t ₁+2 t ₂=4 and 3 t ₁+5 t ₂=2 Solving, we get t₂=10 and t₁=-16 t ₁ t ₂=-160

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