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AP EAMCET201921 Apr 2019Evening ShiftMathematicsVector AlgebraActual

Assertion ( A ) : If a ¯ , b ¯ are two non-collinear vectors then the vector component of b ¯ along the line perpendicular to a ¯ is a ¯ × ( b ¯ × a ¯ ) | a ¯ | 2 . Reason ( R ) : a ¯ × ( b ¯ × c ¯ ) = ( a ¯ · c ¯ ) b ¯ - ( a ¯ · b ¯ ) c ¯ and vector component of b ¯ on c ¯ is b ¯ · c

Options

  1. ABoth ( A ) and ( R ) are true and ( R ) is the correct explanation of ( A )
  2. BBoth ( A ) and ( R ) are true but ( R ) is not the correct explanation of ( A )
  3. C( A ) is true but ( R ) is false
  4. D( A ) is false but ( R ) is true

Correct answer

A. Both ( A ) and ( R ) are true and ( R ) is the correct explanation of ( A )

Step-by-step solution

The vector component b → along the line parallel to a → is a → · b → | a → | a → | a → | The figure below represents the vectors. O A ¯ = a → · b → | a → | a → Now, A B → = O B → - O A → = b → - a → · b → a → 2 a → = ( a → · a → ) b → - ( a → · b → ) a → a → 2 = a → × ( b → × a → ) a → 2 Thus, (A) a

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