Waec Model Questions Vol1 2017 Mathematics Question 16

Practice objective / multiple choice question 16 from the 2017 Waec Model Questions Vol1 Mathematics examination.

Waec Model Questions Vol1 2017 Mathematics Objective / Multiple Choice Hard Difficulty
Question 16 WAEC_MODEL_QUESTIONS_VOL1 • 2017 • MATHEMATICS • objective

Two vectors, \(\mathbf{a} = 3\mathbf{i} + 4\mathbf{j}\) and \(\mathbf{b} = -2\mathbf{i} + \mathbf{j}\), are given. Calculate the magnitude of the vector \(\mathbf{c} = \mathbf{a} + 2\mathbf{b}\) and determine the angle between \(\mathbf{a}\) and \(\mathbf{c}\).

Answer Options

A. Magnitude of \(\mathbf{c}\) is \(\sqrt{50}\) and angle \(\theta = \cos^{-1}\left(\frac{20}{5\sqrt{50}}\right)\).
B. Magnitude of \(\mathbf{c}\) is \(\sqrt{29}\) and angle \(\theta = \cos^{-1}\left(\frac{15}{4\sqrt{29}}\right)\).
Correct Answer C. Magnitude of \(\mathbf{c}\) is \(\sqrt{37}\) and angle \(\theta = \cos^{-1}\left(\frac{21}{5\sqrt{37}}\right)\).
D. Magnitude of \(\mathbf{c}\) is \(\sqrt{45}\) and angle \(\theta = \cos^{-1}\left(\frac{18}{5\sqrt{45}}\right)\).
Correct Answer
C
Correct Option:
Magnitude of \(\mathbf{c}\) is \(\sqrt{37}\) and angle \(\theta = \cos^{-1}\left(\frac{21}{5\sqrt{37}}\right)\).

About This Question

This is Waec Model Questions Vol1 2017 Mathematics Question 16. It is one of the objective questions from the 2017 Waec Model Questions Vol1 Mathematics examination.

Difficulty level: Hard .

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