Answer
The statement makes sense.
Work Step by Step
Assume the two vectors A and B are:
$\mathbf{A}=a\mathbf{i}+b\mathbf{j}+c\mathbf{k}$
And,
$\mathbf{B}=x\mathbf{i}+y\mathbf{j}+z\mathbf{k}$
Now consider the addition operation of vector A and B.
Assume,
$\begin{align}
& \mathbf{C}=\mathbf{A}+\mathbf{B} \\
& =\left( a\mathbf{i}+b\mathbf{j}+c\mathbf{k} \right)+\left( x\mathbf{i}+y\mathbf{j}+z\mathbf{k} \right) \\
& =\left( a+x \right)\mathbf{i}+\left( b+y \right)\mathbf{j}+\left( c+z \right)\mathbf{k}
\end{align}$
The expression $\mathbf{C}=\left( a+x \right)\mathbf{i}+\left( b+y \right)\mathbf{j}+\left( c+z \right)\mathbf{k}$ shows a vector itself. Hence, the vector operations can produce another vector also.
Now consider the dot product of two vectors A and B.
$\begin{align}
& \mathbf{A}\cdot \mathbf{B}=\left( a\mathbf{i}+b\mathbf{j}+c\mathbf{k} \right)\cdot \left( x\mathbf{i}+y\mathbf{j}+z\mathbf{k} \right) \\
& =ax+by+cz
\end{align}$
The expression $\mathbf{A}\cdot \mathbf{B}=ax+by+cz$ has no vector sign in the result. Hence, the dot product of two vectors is a real number.
Therefore, the given statement makes sense.
