Question

If a and b are two vectors perpendicular to each other and |a| = |b| = 1, determine the angle between ( a + b ) and (2a + b ).

Answer 1

Answer:

 Ф = 18°

Explanation:

      A.B = ABcosФ

              cosФ = A.B / AB  ...........( 1 )

A.B = ?

suppose A = ( a + b )         &       B =  (2a + b )

A.B =  ( a + b ) . (2a + b ) = 2a² + b²           as  |a| = |b| = 1

A.B = 3        

|a| = √(1)² + (1)²                  &              IbI = √(2)² + (1)²      

  |a| = √2                           &             IbI = √5

putting vales in Eq.1

Ф = cos∧-1 (3/√10)  = 18°