GCSE Maths Practice: vectors

Question 2 of 10

This question shows how to solve for a vector using vector equations.

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\( \begin{array}{l}\text{Find the vector } \mathbf{d} \text{ if } \mathbf{d} + \begin{pmatrix}2\\-1\end{pmatrix} = \begin{pmatrix}5\\2\end{pmatrix}.\end{array} \)

Choose one option:

Rearrange the equation and subtract component-wise: top-top, bottom-bottom.

To solve for a vector \(\mathbf{d}\) when given \(\mathbf{d} + \mathbf{b} = \mathbf{c}\), rearrange to \(\mathbf{d} = \mathbf{c} - \mathbf{b}\). Subtract corresponding components: top minus top, bottom minus bottom. For \(\mathbf{c} = \begin{pmatrix}5\\2\end{pmatrix}\) and \(\mathbf{b} = \begin{pmatrix}2\\-1\end{pmatrix}\), we get \(5-2=3\) and \(2-(-1)=3\), so \(\mathbf{d} = \begin{pmatrix}3\\3\end{pmatrix}\). This method reinforces component-wise operations and vector algebra skills. Understanding rearrangement is important for physics displacement problems and coordinate geometry. Visualizing vectors on a graph can help ensure the solution is consistent with the intended direction and magnitude. Practicing with multiple examples helps students gain fluency with vector equations and subtraction.