$$\theta = \arctan\left(\frac{-12}{5}\right)$$

Question 1

Given the vector $$\vec{a} = 4\hat{i} + 3\hat{j}$$, what is the unit vector in the direction of $$\vec{a}$$?

Accepted Answer

$$\frac{4}{5}\hat{i} + \frac{3}{5}\hat{j}$$

Question 2

What is the magnitude of the vector $$\vec{b} = 12\hat{i} - 5\hat{j}$$?

Accepted Answer

$$\sqrt{144 + 25}$$

Question 3

Find the unit vector in the direction of $$\vec{b} = 12\hat{i} - 5\hat{j}.$$

Accepted Answer

$$\frac{12}{13}\hat{i} - \frac{5}{13}\hat{j}$$

Question 4

If $$\vec{v} is a $$vector with magnitude $$10$$ and direction $$	heta = 60^\circ$$, what are its components?

Accepted Answer

$$10\cos 60^\circ \hat{i} + 10\sin 60^\circ \hat{j}$$

Question 5

Which of the following best describes a unit vector?

Accepted Answer

A vector with magnitude $$1$$

Question 6

Given $$\vec{a} = 3\hat{i} + 4\hat{j}$$, what is the magnitude of $$\vec{a}$$?

Accepted Answer

$$\sqrt{3^2$ + 4^2$}$$

Question 7

If $$\vec{u} is a $$unit vector in the direction of $$\vec{a} = 8\hat{i} - 6\hat{j}$$, what is $$\vec{u}$$?

Accepted Answer

$$\frac{8}{10}\hat{i} - \frac{6}{10}\hat{j}$$

Question 8

A force of $$20 N $$acts at an angle of $$30^\circ$$ above the horizontal. What is the horizontal component of the force?

Accepted Answer

$$20\cos 30^\circ$$

Question 9

Which of the following is the correct formula for finding the unit vector $$\hat{u} in $$the direction of $$\vec{v}$$?

Accepted Answer

$$\hat{u} = \frac{\vec{v}}{\|\vec{v}\|}$$

Question 10

If $$\vec{a} = 7\hat{i} + 24\hat{j}$$, what is the unit vector in the direction of $$\vec{a}$$?

Accepted Answer

$$\frac{7}{25}\hat{i} + \frac{24}{25}\hat{j}$$

Question 11

A velocity vector is given as $$\vec{v} = 5\hat{i} - 12\hat{j}. $$What is the direction angle $$	heta$$ with respect to the positive $$x-$$axis?

Accepted Answer

$$	heta = \arctan\left(\frac{-12}{5}ight)$$

Unit Vectors and Directions in Trigonometry

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