Match each vector in List I with the angle it makes with the x-axis in List II.

Match each vector in List I with the angle it…

Question 21

MediumOriginal question

Match each vector in List I with the angle it makes with the $x$ -axis in List II.

List I	List II
A. $\hat{i} + \hat{j} + \sqrt{2}\hat{k}$	I. $\frac{\pi}{4}$
B. $\sqrt{2}\hat{i} - \hat{j} + \hat{k}$	II. $\frac{\pi}{2}$
C. $-\hat{i} + \hat{j} - \sqrt{2}\hat{k}$	III. $\frac{\pi}{3}$
D. $2\hat{j} - \hat{k}$	IV. $\frac{2\pi}{3}$

A-III, B-I, C-IV, D-IICorrect answerYour answerA-IV, B-I, C-III, D-IICorrect answerYour answerA-I, B-III, C-IV, D-IICorrect answerYour answerA-III, B-IV, C-I, D-IICorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

$\cos \alpha = \frac{a_1}{\lvert \vec{a} \rvert}$ , and the first three vectors each have magnitude $\sqrt{1 + 1 + 2} = 2$ .
A: $\cos \alpha = \frac{1}{2}$ , $\frac{\pi}{3}$ ; B: $\frac{\sqrt{2}}{2}$ , $\frac{\pi}{4}$ ; C: $-\frac{1}{2}$ , $\frac{2\pi}{3}$ ; D has no $\hat{i}$ part, so $\frac{\pi}{2}$ .

Worth noting

A negative $\hat{i}$ component gives an obtuse angle: $\cos \alpha = -\frac{1}{2}$ is $\frac{2\pi}{3}$ , not $\frac{\pi}{3}$ .

Concept: The angle a vector makes with an axis
Typical timeTypical: 120 s
Your timeYours: —

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Question 21

Explanation