Chapter 1: Vectors, Lines and Planes

Section 1.2: Vector Arithmetic

Example 1.2.4

$$ If $\mathbf{A}\=3 \mathbf{i}\mathbf{-}4 \mathbf{j}\+2 \mathbf{k}$, and $\mathbf{B}\=2 \mathbf{i}\+5 \mathbf{j}-6 \mathbf{k}$, obtain the vectors $3 \mathbf{A}\+4 \mathbf{B}$ and $5 \mathbf{A}-7 \mathbf{B}$. $$ Solution Mathematical Solution $$ Perform componentwise arithmetic to obtain   $3\left[\begin{array}{c}3\\ -4 \\ 2\end{array}\right]\+4\left[\begin{array}{c}2\\ 5\\ -6\end{array}\right]$ = $\left[\begin{array}{c}9\+8\\ -12\+20\\ 6-24\end{array}\right]$ = $\left[\begin{array}{c}17\\ 8\\ -18\end{array}\right]$ and $5\left[\begin{array}{c}3\\ -4\\ 2\end{array}\right] - 7\left[\begin{array}{c}2\\ 5\\ -6\end{array}\right]$ = $\left[\begin{array}{c}15-14\\ -20-35\\ 10\+42\end{array}\right]$ = $\left[\begin{array}{c}1\\ -55\\ 52\end{array}\right]$ $$$$ Maple Solution $$ Data entry •  Keyboard the vector A. (See Table 1.1.1.) •  Context Panel: Assign to a Name≻A $⟨3\,-4\,2⟩$$\stackrel{\text{assign to a name}}{\to }$$A$ •  Keyboard the vector B. (See Table 1.1.1.) •  Context Panel: Assign to a Name≻B $⟨2\,5\,-6⟩$$\stackrel{\text{assign to a name}}{\to }$$B$ Vector arithmetic •  Write the appropriate sum of vectors. •  Context Panel: Evaluate and Display Inline $3 \mathbf{A}\+4 \mathbf{B}$ = $$ •  Write the appropriate sum of vectors. •  Context Panel: Evaluate and Display Inline $5 \mathbf{A}-7 \mathbf{B}$ = $$ $$

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