For the vectors A equals 2i + 3j and B equals 4i minus j, the scalar product A dot B is

Explanation

In component form the dot product is the sum of the products of like components, so (2)(4) plus (3)(minus 1) gives 8 minus 3, which is 5. Only i with i and j with j contribute, because the unit vectors along different axes are perpendicular and their dot products vanish. The value 8 is the first term alone and 11 comes from adding rather than subtracting.