Answer
Scalar multiplication with k is given by $k\mathbf{v}=k{{a}_{1}}\mathbf{i}+k{{b}_{1}}\mathbf{j}$.
Work Step by Step
First, write the vector in terms of $\mathbf{i}\text{ and }\mathbf{j}$.
Then, scalar multiplication with scalar k is found by multiplying the scalar k with the term of $\mathbf{i}$ and multiplying the scalar k with the term of $\mathbf{j}$.
Then, the vector is given by $k\mathbf{v}$.
If $\mathbf{v}={{a}_{1}}\mathbf{i}+{{b}_{1}}\mathbf{j}$, then scalar multiplication with k is given by $k\mathbf{v}$.
$k\mathbf{v}=k{{a}_{1}}\mathbf{i}+k{{b}_{1}}\mathbf{j}$
Example: Information: Consider the vector $\mathbf{v}=2\mathbf{i}+6\mathbf{j}$ and $k=3$.
Then, scalar multiplication with k gives $k\mathbf{v}$.
$\begin{align}
& k\mathbf{v}=3\left( 2\mathbf{i}+6\mathbf{j} \right) \\
& =\left( 3\cdot 2 \right)\mathbf{i}+\left( 3\cdot 6 \right)\mathbf{j} \\
& =6\mathbf{i}+18\mathbf{j}
\end{align}$
