Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202017 Sep 2020Evening ShiftMathematicsVector AlgebraActual

If ( a + b + c =0 ) and (| a |=3,| b |=5,| c |=7 ), then the angle between ( a ) and ( b ) is ........

Options

  1. A(30^ )
  2. B(120^ )
  3. C(90^ )
  4. D(60^ )

Correct answer

D. (60^ )

Step-by-step solution

Given, ( a + b + c = 0 ) ( array lllll & ( a + b )=- c & ( a + b )^2= c ^2 & a ^2+ b ^2+2 a b = c ^2 & 2 a b = c ^2- a ^2- b ^2 array ) As square of a vector (= ) square of its magnitude, ( aligned & 2 a b =49-9-25 & 2 a b =15 & = 15 2 3 5 & = ⁻¹ ( 1 2 )=60^ 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