Neco 2018 Mathematics Question 31

Practice objective / multiple choice question 31 from the 2018 Neco Mathematics examination.

Neco 2018 Mathematics Objective / Multiple Choice Hard Difficulty
Question 31 NECO • 2018 • MATHEMATICS • objective

Given two vectors \(\mathbf{a}\) and \(\mathbf{b}\) in the plane such that \(|\mathbf{a}| = 5\), the vector \(\mathbf{a} + \mathbf{b}\) is perpendicular to \(\mathbf{a}\), and \(|\mathbf{a} + \mathbf{b}| = 13\). Find the magnitude \(|\mathbf{b}|\) and the angle between \(\mathbf{a}\) and \(\mathbf{b}\) (to the nearest degree).

Answer Options

A. Magnitude \(|\mathbf{b}| = \sqrt{144}\) (≈12) and angle ≈105°
B. Magnitude \(|\mathbf{b}| = \sqrt{225}\) (≈15) and angle ≈120°
C. Magnitude \(|\mathbf{b}| = \sqrt{169}\) (≈13) and angle ≈90°
Correct Answer D. Magnitude \(|\mathbf{b}| = \sqrt{194}\) (≈13.93) and angle ≈111°
Correct Answer
D
Correct Option:
Magnitude \(|\mathbf{b}| = \sqrt{194}\) (≈13.93) and angle ≈111°

About This Question

This is Neco 2018 Mathematics Question 31. It is one of the objective questions from the 2018 Neco Mathematics examination.

Difficulty level: Hard .

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