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MHT CET202410 May 2024Evening ShiftMathematicsVector AlgebraActual

If a = j - k and c = i - j - k , then the vector b satisfying a b + c = 0 and a b =3 is

Options

  1. A- i +2 j -2 k
  2. B- i + j - k
  3. C- i - j + k
  4. Di + j + k

Correct answer

B. - i + j - k

Step-by-step solution

Given: - a = j - k , - c = i - j - k , - Find b such that ( a b )+ c =0 and a b = 3 . Write b in component form: b =p i +q j +r k Compute a b : aligned a & =(0,1,-1), b =(p, q, r) a b = | array ccc i & j & k 0 & 1 & -1 p & q & r array | & = i (1 r-(-1) q)- j (0 r-(-1) p)+ k (0 q-1 p) a & b =(r+q) i -(-p) j -p k a & b =(r+q) i +p j -p k aligned Use ( a b )+ c =0 : (r+q) i +p j -p k +( i - j - k )=0 Equating components: - i -component: r+q+1=0 r+q=-1 , - j -component: p-1=0 p=1 , - k -component: -p-1=0 p=-1 . Solve a

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