Waec Model Questions Vol1 2021 Mathematics Question 19

Practice objective / multiple choice question 19 from the 2021 Waec Model Questions Vol1 Mathematics examination.

Waec Model Questions Vol1 2021 Mathematics Objective / Multiple Choice Hard Difficulty
Question 19 WAEC_MODEL_QUESTIONS_VOL1 • 2021 • MATHEMATICS • objective

Given the vectors \(\mathbf{a}=3\mathbf{i}-4\mathbf{j}+\mathbf{k}\) and \(\mathbf{b}=-\mathbf{i}+2\mathbf{j}+2\mathbf{k}\): (i) Find the magnitude of \(\mathbf{a}\). (ii) Determine the angle between \(\mathbf{a}\) and \(\mathbf{b}\) (to the nearest degree). (iii) Find a vector \(\mathbf{c}\) that is perpendicular to both \(\mathbf{a}\) and \(\mathbf{b}\) and has magnitude 5. Express \(\mathbf{c}\) in unit‑vector form.

Answer Options

A. -\frac{55}{\sqrt{153}}\mathbf{i} -\frac{40}{\sqrt{153}}\mathbf{j}+\frac{5}{\sqrt{153}}\mathbf{k}
B. -\frac{45}{\sqrt{153}}\mathbf{i} -\frac{30}{\sqrt{153}}\mathbf{j}+\frac{15}{\sqrt{153}}\mathbf{k}
Correct Answer C. -\frac{50}{\sqrt{153}}\mathbf{i} -\frac{35}{\sqrt{153}}\mathbf{j}+\frac{10}{\sqrt{153}}\mathbf{k}
D. -\frac{50}{\sqrt{152}}\mathbf{i} -\frac{35}{\sqrt{152}}\mathbf{j}+\frac{10}{\sqrt{152}}\mathbf{k}
Correct Answer
C
Correct Option:
-\frac{50}{\sqrt{153}}\mathbf{i} -\frac{35}{\sqrt{153}}\mathbf{j}+\frac{10}{\sqrt{153}}\mathbf{k}

About This Question

This is Waec Model Questions Vol1 2021 Mathematics Question 19. It is one of the objective questions from the 2021 Waec Model Questions Vol1 Mathematics examination.

Difficulty level: Hard .

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