## Exam-Style Question on Vectors## A mathematics exam-style question with a worked solution that can be revealed gradually |

Question id: 634. This question is similar to one that appeared on an IB AA Higher paper in 2022. The use of a calculator is allowed.

Consider the vectors \(\mathbf{a}\) and \(\mathbf{b}\) such that \(\mathbf{a} = \begin{pmatrix} 16 \\ -12 \end{pmatrix} \) and \( |\mathbf{b}| = 11\).

(a) Find the possible range of values for \(|\mathbf{a+b}|\).

Consider the vector \(\mathbf{p}\) such that \(\mathbf{p=a+b}\).

(b) Given that \(|\mathbf{a+b}|\) is a minimum, find \(\mathbf{p}\).

Consider the vector q such that \(\mathbf{q} = \begin{pmatrix}x \\ y \end{pmatrix} \) , where \(x,y \in \mathbb{R} \).

(c) Find \(\mathbf{q}\) such that \(\mathbf{|q| = |b|}\) and \(\mathbf{q}\) is perpendicular to \(\mathbf{a}\).

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