Mathematics for IGCSE & O level - Vectors (Section 2 - No. 7)
If \(\vec{a} = \begin{pmatrix} 1 \\ 2 \end{pmatrix}\) and \(\vec{b} = \begin{pmatrix} 3 \\ -1 \end{pmatrix}\), which of the following expressions correctly represents the calculation for 3\(\vec{a}\) + 2\(\vec{b}\)?
3\(\begin{pmatrix} 1 \\ 2 \end{pmatrix}\) + 2\(\begin{pmatrix} 3 \\ -1 \end{pmatrix}\)
\(\begin{pmatrix} 3(1) + 2(3) \\ 2 + (-1) \end{pmatrix}\)
3\(\begin{pmatrix} 1 \\ 2 \end{pmatrix}\) - 2\(\begin{pmatrix} 3 \\ -1 \end{pmatrix}\)
\(\begin{pmatrix} 1 + 3 \\ 2 - 1 \end{pmatrix}\)
Explanation
You must scalar multiply then add the vector quantities.
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