Mathematics for IGCSE & O level - Vectors (Section 2 - No. 3)
If \(\vec{a} = \begin{pmatrix} 1 \\ 2 \end{pmatrix}\) and \(\vec{b} = \begin{pmatrix} -3 \\ 1 \end{pmatrix}\), what is \(2\vec{a} - \vec{b}\)?
\(\begin{pmatrix} 5 \\ 3 \end{pmatrix}\)
\(\begin{pmatrix} 5 \\ 5 \end{pmatrix}\)
\(\begin{pmatrix} -1 \\ 3 \end{pmatrix}\)
\(\begin{pmatrix} -5 \\ 3 \end{pmatrix}\)
Explanation
2a - b = 2\(\begin{pmatrix} 1 \\ 2 \end{pmatrix}\) - \(\begin{pmatrix} -3 \\ 1 \end{pmatrix}\) = \(\begin{pmatrix} 2 \\ 4 \end{pmatrix}\) - \(\begin{pmatrix} -3 \\ 1 \end{pmatrix}\) = \(\begin{pmatrix} 5 \\ 3 \end{pmatrix}\)
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