Gce Model Questions Vol1 2017 Mathematics Question 36

Practice objective / multiple choice question 36 from the 2017 Gce Model Questions Vol1 Mathematics examination.

Gce Model Questions Vol1 2017 Mathematics Objective / Multiple Choice Hard Difficulty
Question 36 GCE_MODEL_QUESTIONS_VOL1 • 2017 • MATHEMATICS • objective

Given two vectors \(\mathbf{a}\) and \(\mathbf{b}\) in a plane such that \(|\mathbf{a}| = 5\), \(|\mathbf{b}| = 8\) and \(\mathbf{a}\cdot\mathbf{b}=20\). Find (i) the exact magnitude of the vector \(3\mathbf{a}-2\mathbf{b}\) and (ii) the cosine of the angle between \(3\mathbf{a}-2\mathbf{b}\) and \(\mathbf{a}\).

Answer Options

A. |3\mathbf{a}-2\mathbf{b}| = \sqrt{225}, \; \cos\phi = \frac{5}{\sqrt{225}}
B. |3\mathbf{a}-2\mathbf{b}| = \sqrt{256}, \; \cos\phi = \frac{8}{\sqrt{256}}
Correct Answer C. |3\mathbf{a}-2\mathbf{b}| = \sqrt{241}, \; \cos\phi = \frac{7}{\sqrt{241}}
D. |3\mathbf{a}-2\mathbf{b}| = \sqrt{200}, \; \cos\phi = \frac{6}{\sqrt{200}}
Correct Answer
C
Correct Option:
|3\mathbf{a}-2\mathbf{b}| = \sqrt{241}, \; \cos\phi = \frac{7}{\sqrt{241}}

About This Question

This is Gce Model Questions Vol1 2017 Mathematics Question 36. It is one of the objective questions from the 2017 Gce Model Questions Vol1 Mathematics examination.

Difficulty level: Hard .

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