Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202520 Apr 2025Evening ShiftMathematicsVector AlgebraActual

In a triangle ABC with usual notations if | BC |=8,| CA |=7,| AB |=10 then the projection of AB on AC is

Options

  1. A14 85 units
  2. B1 85 units
  3. C85 14 units
  4. D7 85 units

Correct answer

C. 85 14 units

Step-by-step solution

The projection of AB onto AC is given by AB AC | AC | . Using the law of cosines to find the angle between the vectors: a^2 = b^2 + c^2 - 2bc A where a = 8 , b = 7 , and c = 10 . This yields 64 = 49 + 100 - 140 A , so 140 A = 85 and A = 85 140 . The dot product becomes AB AC = | AB || AC | A = 70 85 140 = 85 2 . Substituting into the projection formula: 85/2 7 = 85 14 . The projection length is 85 14 , matching option C .

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