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If $\mathbf{a}=\hat{\mathbf{i}}+4 \hat{\mathbf{j}}, \mathbf{b}=2 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}, \mathbf{c}=5 \hat{\mathbf{i}}+9 \hat{\mathbf{j}}$, then $\mathbf{c}$ is equal to
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$3 \mathbf{a}+\mathbf{b}$
$\begin{aligned} 3 \mathbf{a}+\mathbf{b} & =3(\hat{\mathbf{i}}+4 \hat{\mathbf{j}})+2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}} \\ & =3 \hat{\mathbf{i}}+12 \hat{\mathbf{j}}+2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}=5 \hat{\mathbf{i}}+9 \hat{\mathbf{j}}=\mathbf{c}\end{aligned}$
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