# Chapter 6 - Section 6.6 - Vectors - Exercise Set - Page 782: 34

$4\mathbf{w}-3\mathbf{v}=5\mathbf{i}-45\mathbf{j}$

#### Work Step by Step

Here, \begin{align} & {{a}_{1}}=-3 \\ & {{a}_{2}}=-1 \\ & {{b}_{1}}=7 \\ & {{b}_{2}}=-6 \end{align} \begin{align} & {{k}_{1}}=3 \\ & {{k}_{2}}=4 \\ \end{align} Therefore, the value of $3\mathbf{v},4\mathbf{w}$ is, \begin{align} & 3\mathbf{v}=\left[ 3\times \left( -3 \right) \right]\mathbf{i}+\left[ 3\times 7 \right]\mathbf{j} \\ & =-9\mathbf{i}+21\mathbf{j} \end{align} \begin{align} & 4\mathbf{w}=\left[ 4\times \left( -1 \right) \right]\mathbf{i}+\left[ 4\times \left( -6 \right) \right]\mathbf{j} \\ & =-4\mathbf{i}-24\mathbf{j} \end{align} Subtract $3\mathbf{v}$ from $4\mathbf{w}$ to get, \begin{align} & 4\mathbf{w}-3\mathbf{v}=\left[ -4-\left( -9 \right) \right]\mathbf{i}+\left[ -24-\left( 21 \right) \right]\mathbf{j} \\ & =5\mathbf{i}-45\mathbf{j} \end{align}

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