Neco 2025 Further Mathematics Question 22
Practice objective / multiple choice question 22 from the 2025 Neco Further Mathematics examination.
The vectors \(\mathbf{a},\mathbf{b},\mathbf{c}\) in three‑dimensional space satisfy \(|\mathbf{a}|=3\), \(|\mathbf{b}|=4\), \(|\mathbf{c}|=5\), \(\mathbf{a}\cdot\mathbf{b}=6\) and \(\mathbf{b}\cdot\mathbf{c}=8\). It is also given that \(\mathbf{a}+\mathbf{b}+\mathbf{c}\) is orthogonal to \(\mathbf{a}\).\n\n(a) Find the value of \(\mathbf{a}\cdot\mathbf{c}\).\n(b) Let \(\mathbf{d}= \mathbf{a}+2\mathbf{b}\). Determine the magnitude \(|\mathbf{d}|\) and the angle between \(\mathbf{d}\) and \(\mathbf{c}\) (to one decimal place in degrees).
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This is Neco 2025 Further Mathematics Question 22. It is one of the objective questions from the 2025 Neco Further Mathematics examination.
Difficulty level: Hard .
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