Evaluate the dot product a⃗ ⋅b⃗ of a⃗ = 3i^-8j^ and b⃗ = - 2i^-6j^.

The "dot product" of two vectors has several different formulas.

Since you are given the x - and y-coordinates of both vectors a and b, we can apply the formula

a dot b = ax*bx + ay*by, where ax=x-component of vector a, by=y comp of vector b, and so on.

So, for the problem at hand, ax * bx + ay * by becomes

3 (-2) + (-8) (-6) = - 6 + 48 = 42 (answer). Note that the dot product (or "scalar product" is itself a scalar.