Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202423 May 2024Morning ShiftMathematicsVector AlgebraActual

The length of the internal bisector of angle A in ABC with vertices A(4,7,8), B(2,3,4) and C(2,5,7) is

Options

  1. A1 3 29
  2. B2 3 29
  3. C2 3 34
  4. D4 3 34

Correct answer

C. 2 3 34

Step-by-step solution

Let A D be the bisector of angle A met B C at D . Then D divides B C in ratio A B: A C aligned & A B= 4+16+16 =6, A C= 4+4+1 =3 & D= ( 6+12 6+3 , 9+30 6+3 , 12+42 6+3 )= (2, 13 3 , 6 ) & A D= (-2)^2+ (- 8 3 )^2+(-2)^2 = 136 9 = 2 34 3 . 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 AP EAMCET PYQs