Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Manipal MET2010MathematicsVector Algebra

Consider a tetrahedron with faces F₁, F₂, F₃, F₄ . Let V ₁, V ₂, V ₃, V ₄ be the vectors whose magnitudes are respectively equal to areas of F₁, F₂, F₃, F₄ and whose directions are perpendicular to these faces in outward direction, then | V ₁+ V ₂+ V ₃+ V ₄ | equals

Options

  1. A1
  2. B4
  3. C0
  4. DNone of these

Correct answer

C. 0

Step-by-step solution

We have, aligned & v ₁= 1 2 ( a b ), v ₂= 1 2 ( b c ), v ₃= 1 2 ( c a ) & and v ₄= 1 2 ( c - a ) ( b - a ) & aligned & v ₁+ V ₂+ v ₃+ v ₄= 1 2 ( a b + b c + c a + c b - c a - a b )= 0 & | V ₁+ V ₂+ V ₃+ V ₄ |= 0 aligned 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