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MHT CET202314 May 2023Evening ShiftMathematicsVector AlgebraActual

Let a = i +2 j - k and b = i + j - k be two vectors. If c is a vector such that b c = b a and c a =0 , then c b is

Options

  1. A1 2
  2. B3 2
  3. C-3 2
  4. D-1 2

Correct answer

D. -1 2

Step-by-step solution

aligned & Given, b c = b a & b ( c - a )= 0 aligned b is parallel to ( c - a ) . aligned & c - a = b for some scalar & c = a + b ... (i)) & c a = a a + ( b a ) aligned 0=| a |^2+ ( b a ), [ c a =0 (given) ] aligned & 0=6 4 & =- 3 2 aligned Substitutifing the value of in (i), we get aligned c & =( i +2 j - k )- 3 2 ( i + j - k ) = & - 1 2 ( i - j - k ) c b & =- 1 2 ( i - j - k ) ( i + j - k ) & =- 1 2 (1-1+1)=- 1 2 aligned

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