Mathematics for IGCSE & O level - Vectors (Section 2 - No. 27)
Given \(\vec{a} = \begin{pmatrix} 2 \\ 1 \end{pmatrix}\) and \(\vec{b} = \begin{pmatrix} 1 \\ 3 \end{pmatrix}\), which of the following represents \(\vec{a} + 2\vec{b}\)?
\(\begin{pmatrix} 4 \\ 7 \end{pmatrix}\)
\(\begin{pmatrix} 4 \\ 3 \end{pmatrix}\)
\(\begin{pmatrix} 0 \\ -5 \end{pmatrix}\)
\(\begin{pmatrix} 3 \\ 4 \end{pmatrix}\)
Explanation
a + 2b = \(\begin{pmatrix} 2 \\ 1 \end{pmatrix}\) + 2\(\begin{pmatrix} 1 \\ 3 \end{pmatrix}\) = \(\begin{pmatrix} 2 \\ 1 \end{pmatrix}\) + \(\begin{pmatrix} 2 \\ 6 \end{pmatrix}\) = \(\begin{pmatrix} 4 \\ 7 \end{pmatrix}\)
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