Neco 2023 Mathematics Question 26

Practice objective / multiple choice question 26 from the 2023 Neco Mathematics examination.

Neco 2023 Mathematics Objective / Multiple Choice Hard Difficulty
Question 26 NECO • 2023 • MATHEMATICS • objective

Given non‑zero vectors \\(\\mathbf{a}\\) and \\(\\mathbf{b}\\) with magnitudes \\(|\\mathbf{a}|=5\\) and \\(|\\mathbf{b}|=3\\). It is known that the vector \\(\\mathbf{a}+2\\mathbf{b}\\) is perpendicular to \\(3\\mathbf{a}-\\mathbf{b}\\). Find the angle between \\(\\mathbf{a}\\) and \\(\\mathbf{b}\\) (in degrees, to one decimal place) and then compute the magnitude of \\(\\mathbf{a}-\\mathbf{b}\\).

Answer Options

A. Angle \\(\\theta = \\arccos(-7\\/25) \\approx 115.9^{\\circ}\\); \\(|\\mathbf{a}-\\mathbf{b}| = \\frac{2\\sqrt{355}}{5}\\)
B. Angle \\(\\theta = \\arccos(19\\/25) \\approx 41.4^{\\circ}\\); \\(|\\mathbf{a}-\\mathbf{b}| = \\frac{2\\sqrt{355}}{5}\\)
Correct Answer C. Angle \(\theta = \arccos(-19/25) \approx 138.6^{\circ}\); \(|\mathbf{a}-\mathbf{b}| = \frac{2\sqrt{355}}{5}\)
D. Angle \\(\\theta = \\arccos(-19\\/25) \\approx 138.6^{\\circ}\\); \\(|\\mathbf{a}-\\mathbf{b}| = \\frac{\\sqrt{355}}{5}\\)
Correct Answer
C
Correct Option:
Angle \(\theta = \arccos(-19/25) \approx 138.6^{\circ}\); \(|\mathbf{a}-\mathbf{b}| = \frac{2\sqrt{355}}{5}\)

About This Question

This is Neco 2023 Mathematics Question 26. It is one of the objective questions from the 2023 Neco Mathematics examination.

Difficulty level: Hard .

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