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Manipal MET2013MathematicsVector Algebra

If a i = a ( j + i )= a ( i + j + k ) , then a is equal to

Options

  1. Ai
  2. Bk
  3. Cj
  4. D(i+j+k)

Correct answer

A. i

Step-by-step solution

Let a =x i +y j +z k then, a i =(x i +y j +z k ) i =x and a ( i + j )=(x i +y j + zk ) ( i + j )=x+y and a ( i + j + k )=(x i+y j +z k ) ( i + j + k )=x+y+z Given that a j = a ( j + I )= a ( l + j + k ) x=x+y=x+y+z Now, x=x+y y=0 and x+y=x+y+z z=0 array ll Hence; & x=1 & a=I array

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