Gegeven is de vector \(\overrightarrow{a} = \begin{pmatrix}-5 \\ -2\end{pmatrix} \text{.}\)
1p
Bereken de lengte van \(\overrightarrow{a} \text{.}\)
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\(\begin{vmatrix}\overrightarrow{a}\end{vmatrix} = \sqrt{(-5)^{2} + (-2)^{2}} = \sqrt{29} \text{.}\)
1p
Gegeven is de vector \(\overrightarrow{a} = \begin{pmatrix}-6 \\ -1\end{pmatrix} \text{.}\)
1p
Bereken de vector die je krijgt wanneer je \(\overrightarrow{a}\) linksom draait over \(90\degree \text{.}\)
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\(\overrightarrow{a}_{\text{L}} = \begin{pmatrix}1 \\ -6\end{pmatrix} \text{.}\)
1p
Gegeven is de vector \(\overrightarrow{a} = \begin{pmatrix}-3 \\ -1\end{pmatrix} \text{.}\)
1p
Bereken \(5 ⋅ \overrightarrow{a} \text{.}\)
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\(5 ⋅ \overrightarrow{a} = 5 ⋅ \begin{pmatrix}-3 \\ -1\end{pmatrix} = \begin{pmatrix}-15 \\ -5\end{pmatrix} \text{.}\)
1p
Gegeven zijn de vectoren \(\overrightarrow{a} = \begin{pmatrix}-4 \\ -2\end{pmatrix}\) en \(\overrightarrow{b} = \begin{pmatrix}5 \\ -1\end{pmatrix} \text{.}\)
1p
Bereken het inproduct van de vectoren \(\overrightarrow{a}\) en \(\overrightarrow{b} \text{.}\)
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\(\overrightarrow{a} ⋅ \overrightarrow{b} = -4 ⋅ 5 - 2 ⋅ -1 = -18 \text{.}\)
1p
Gegeven zijn de vectoren \(\overrightarrow{a} = \begin{pmatrix}-1 \\ 4\end{pmatrix}\) en \(\overrightarrow{b} = \begin{pmatrix}0 \\ -7\end{pmatrix} \text{.}\)
1p
Bereken \(\overrightarrow{a} + \overrightarrow{b} \text{.}\)
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\(\overrightarrow{a} + \overrightarrow{b} = \begin{pmatrix}-1 \\ 4\end{pmatrix} + \begin{pmatrix}0 \\ -7\end{pmatrix} = \begin{pmatrix}-1 \\ -3\end{pmatrix} \text{.}\)
1p
Gegeven zijn de vectoren \(\overrightarrow{a} = \begin{pmatrix}4 \\ -1\end{pmatrix}\) en \(\overrightarrow{b} = \begin{pmatrix}3 \\ -6\end{pmatrix} \text{.}\)
1p
Bereken \(7 \overrightarrow{a} - 5 \overrightarrow{b} \text{.}\)
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\(7 \overrightarrow{a} - 5 \overrightarrow{b} = 7 \begin{pmatrix}4 \\ -1\end{pmatrix} - 5 \begin{pmatrix}3 \\ -6\end{pmatrix} = \begin{pmatrix}13 \\ 23\end{pmatrix} \text{.}\)
1p
Gegeven zijn de punten \(A (-4 , 1)\) en \(B (3 , 7) \text{.}\) Het punt \(C\) is het midden van lijnstuk \(A\kern{-.8pt}B \text{.}\)
1p
Bereken vector \(\overrightarrow{c} \text{.}\)
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\(\overrightarrow{c} = {1 \over 2} ⋅ (\overrightarrow{a} + \overrightarrow{b}) = {1 \over 2} ⋅ (\begin{pmatrix}-4 \\ 1\end{pmatrix} + \begin{pmatrix}3 \\ 7\end{pmatrix}) = {1 \over 2} ⋅ \begin{pmatrix}-1 \\ 8\end{pmatrix} = \begin{pmatrix}-\frac{1}{2} \\ 4\end{pmatrix} \text{.}\)
1p
Gegeven zijn de punten \(A (5 , 6)\) en \(B (3 , 4) \text{.}\)
1p
Bereken vector \(\overrightarrow{AB} \text{.}\)
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\(\overrightarrow{AB} = \overrightarrow{b} - \overrightarrow{a} = \begin{pmatrix}3 \\ 4\end{pmatrix} - \begin{pmatrix}5 \\ 6\end{pmatrix} = \begin{pmatrix}-2 \\ -2\end{pmatrix} \text{.}\)
1p