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AP EAMCET202017 Sep 2020Evening ShiftMathematicsVector AlgebraActual

Let ( u , v ) and ( w ) be three vectors in (R^3 ). Then, any vector (Z R ^3 ) can be written as (z=a u +b v +c w ) for some scalars (a, b ) and (c ) if and only if

Options

  1. AEach pair of ( u , v ) and ( w ) are not parallel
  2. BEach of ( u , v ) and ( w ) can be written as a linear combination of the other two
  3. CAll have different magnitude and directions
  4. DNone of the options are correct

Correct answer

D. None of the options are correct

Step-by-step solution

As given vector (u, v ) and ( w ) given may be not parallel but they may be antiparallel So, ( z a u +b v +c w ) So first is incorrect. Also, if ( u = v + w ) ( gathered v = u + w w = u + v gathered ) Then, ( u + v + w =2( u + v + w ) ) ( u + v + w = 0 z ) So, option (b) is incorrect. Similarly, option (c) is incorrect.

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