Neco 2022 Mathematics Question 43

Practice objective / multiple choice question 43 from the 2022 Neco Mathematics examination.

Neco 2022 Mathematics Objective / Multiple Choice Hard Difficulty
Question 43 NECO • 2022 • MATHEMATICS • objective

In the plane, vectors \(\mathbf{a}\) and \(\mathbf{b}\) satisfy \(|\mathbf{a}| = 5\), \(|\mathbf{b}| = 8\) and the angle between them is \(60^{\circ}\). Let \(\mathbf{c} = 2\mathbf{a} - \mathbf{b}\). Find (i) the magnitude of \(\mathbf{c}\); (ii) a unit vector \(\mathbf{u}\) that is parallel to \(\mathbf{c}\); (iii) the area of the parallelogram formed by \(\mathbf{a}\) and \(\mathbf{c}\).

Answer Options

Correct Answer A. |\mathbf{c}| = 2\sqrt{21} (≈9.2); \mathbf{u}=\frac{2\mathbf{a}-\mathbf{b}}{2\sqrt{21}}; area = 20\sqrt{3} (≈34.6)
B. |\\mathbf{c}| = 2\\sqrt{61} (≈15.6); \\mathbf{u}=\\frac{2\\mathbf{a}-\\mathbf{b}}{2\\sqrt{61}}; area = 30\\sqrt{3} (≈51.96)
C. |\\mathbf{c}| = \\sqrt{44} (≈6.6); \\mathbf{u}=\\frac{2\\mathbf{a}-\\mathbf{b}}{\\sqrt{44}}; area = 10\\sqrt{3} (≈17.3)
D. |\\mathbf{c}| = 10 (≈10.0); \\mathbf{u}=\\frac{2\\mathbf{a}-\\mathbf{b}}{10}; area = 25\\sqrt{3} (≈43.3)
Correct Answer
A
Correct Option:
|\mathbf{c}| = 2\sqrt{21} (≈9.2); \mathbf{u}=\frac{2\mathbf{a}-\mathbf{b}}{2\sqrt{21}}; area = 20\sqrt{3} (≈34.6)

About This Question

This is Neco 2022 Mathematics Question 43. It is one of the objective questions from the 2022 Neco Mathematics examination.

Difficulty level: Hard .

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