The dot product of two vectors a and b is given by the formula:

a · b = |a| |b| cos(θ)

Where:
– a · b is the dot product of vectors a and b.
– |a| and |b| are the magnitudes (lengths) of vectors a and b, respectively.
– θ is the angle between the two vectors.

Since a and b are perpendicular, the angle θ between them is 90 degrees. The cosine of 90 degrees is 0:

cos(90°) = 0

Thus, the dot product becomes:

a · b = |a| |b| * 0 = 0

Therefore, the dot product of two perpendicular vectors a and b is zero.