# Chapter 6 - Section 6.6 - Vectors - Exercise Set - Page 782: 54

$-33i+13j$.

#### Work Step by Step

Put $u=-2i+3j,v=6i-j$, $w=-3i$ in the expression $3u-\left( 4v-w \right)$. Then, \begin{align} & 3u-\left( 4v-w \right)=3\left( -2i+3j \right)-\left( 4\left( 6i-j \right)-\left( -3i \right) \right) \\ & =-6i+9j-\left( \left( 24i-4j \right)+3i \right) \\ & =-6i+9j-27i+4j \\ & =-33i+13j \end{align}

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