Neco 2021 Further Mathematics Question 12
Practice objective / multiple choice question 12 from the 2021 Neco Further Mathematics examination.
In three‑dimensional space let \( \mathbf{a}= (3,\,4,\,0) \). A vector \( \mathbf{b}= (x,\,y,\,z) \) satisfies \( |\mathbf{b}| = 7 \) and \( \mathbf{a}\cdot\mathbf{b}=14 \).\n(a) Find the magnitude of \( \mathbf{c}=\mathbf{a}\times\mathbf{b} \).\n(b) Determine a unit vector \( \mathbf{u} \) that is orthogonal to \( \mathbf{a} \) and makes an angle of \(30^{\circ}\) with \( \mathbf{c} \). Give the components of \( \mathbf{u} \) correct to two decimal places.
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About This Question
This is Neco 2021 Further Mathematics Question 12. It is one of the objective questions from the 2021 Neco Further Mathematics examination.
Difficulty level: Medium .
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