Find a ⋅ b. a = 10i + 9j, b = 4i + 3j

Solution:

Vector a = 10i + 9j

Vector b = 4i + 3j

If two vectors  u = u₁i + u₂j and v = v₁i + v₂j then the dot product of the two vectors is given by

u.v = ( u₁v₁)i + (u₂v₂)j

Therefore

a.b =  (10  ×  4 )i + (3 × 9)j

a.b =  40i  +  27j

Find a ⋅ b. a = 10i + 9j, b = 4i + 3j

Summary:

 If a = 10i + 9j, b = 4i + 3j then  a ⋅ b is equal to a.b =  40i  +  27j.