Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
KCET2013MathematicsVector Algebra

If a =(1,2,3), b =(2,-1,1), c =(3,2,1) and a ( b c )= a + b + c , then

Options

  1. A=1, =10, =3
  2. B=0, =10, =-3
  3. C+ + =8
  4. D= = =0

Correct answer

B. =0, =10, =-3

Step-by-step solution

Given, a=(1,2,3)=i+2 j+3 kb=(2,-1,1)=2 i-j+k array ll and & c=(3,2,1)=3 i+2 j+k Now, & a (b c)= a+ b+ c & (a c) b-(a b) c= a+ b+ c & (i+2 j+3 k) (3 i+2 j+k) b & - (i+2 j+3 k) (2 i-j+k) c array aligned &= a+ b+ c &(3+4+3) b-(2-2+3) c= a+ b+ c & 0 a+10 b-3 c= a+ b+ c aligned On comparing, we get =0, =10 and =-3

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 KCET PYQs