If a and b are

Dear student,

given , $|a+b| = |a|$
            (|a + b|)² = |a|²           [ squaring on both sides
  (a+b)·(a+b) = a·a
a·a + b·a + a·b + b·b = a·a
2a·b + b·b = 0                       [since b·a=a·b
(2a+b)·b=0
since the dot product is zero, so angle should be 90 degrees between these two vectors.
thus, vector (2a+b) is perpendicular to vector b.

Regards

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