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COMEDK2023MathematicsVector Algebra

a =2 i + j - k , b = i - j and c =5 i - j + k , then unit vector parallel to a + b - c but in opposite direction is

Options

  1. A1 3 (2 i - j +2 k )
  2. B1 2 (2 i - j +2 k )
  3. C1 3 (2 i - j -2 k )
  4. DNone of these

Correct answer

A. 1 3 (2 i - j +2 k )

Step-by-step solution

Given, a =2 i + j - k , b = i - j and c =5 i - j + k aligned : a + b - c & =(2+1-5) i +(1-1+1) j +(-1+0-1) k & =-2 i + j -2 k =-(2 i - j +2 k ) aligned Now, the unit vector in the direction of a + b - c be -(2 i - j +2 k ) 2^2+(-1)^2+2^2 =- 1 3 (2 i - j +2 k ) The required unit vector be 1 3 (2 i - j +2 k ) .

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