$$\theta = \arctan\left(\frac{-3}{4}\right)$$

Question 1

A vector is defined as:

Accepted Answer

A quantity having both size and direction.

Question 2

Which of the following statements about unit vectors is correct?

Accepted Answer

Unit vectors have magnitude 1 and no units.

Question 3

A vector $$\vec{A}$$ has components $$A_x = -3$$ and $$A_y = 2. $$What is the magnitude of $$\vec{A}$$?

Accepted Answer

$$\sqrt{(-3)^2$ + 2^2$} = \sqrt{9 + 4} = \sqrt{13}$$

Question 4

A bird flies 100 m due east, then 50 m northwest (45° north of west). What is the x-component of the bird’s net displacement?

Accepted Answer

$$100 + 50 \cos(135^\circ)$$

Question 5

If a vector $$\vec{B}$$ has components $$B_x = 4$$ and $$B_y = -3$$, what is the direction angle $$	heta$$ measured from the positive x-axis?

Accepted Answer

$$	heta = \arctan\left(\frac{-3}{4}ight)$$

Question 6

A rabbit runs at 10.0 m/s, 40.0° north of west. What is the y-component of its velocity?

Accepted Answer

$$10.0 \sin(40.0^\circ)$$

Question 7

Which method is NOT used for vector addition according to the chapter?

Accepted Answer

Numerical addition

Question 8

A force of 720 N acts at 15° to the humerus. If the humerus is tilted 30° below horizontal, what is the component of force parallel to the bone?

Accepted Answer

$$720 \cos(15^\circ)$$

Question 9

If $$\vec{A} = 2\hat{i} + 3\hat{j}$$ and $$\vec{B} = -1\hat{i} + 4\hat{j}$$, what is $$\vec{A} + \vec{B}$$?

Accepted Answer

$$1\hat{i} + 7\hat{j}$$

Question 10

Which statement about vector subtraction is correct?

Accepted Answer

Subtracting a vector is equivalent to adding its negative.

Question 11

A vector $$\vec{C}$$ has magnitude 5 and points 60° above the x-axis. What are its components?

Accepted Answer

$$C_x = 5 \cos(60^\circ)$$, $$C_y = 5 \sin(60^\circ)$$

Question 12

Which of the following is NOT a property of vectors?

Accepted Answer

Vectors are fully described by a single number.

Question 13

If a vector points left and down, what must be true about its components?

Accepted Answer

Both x- and y-components are negative.

Question 14

A hiker walks 4 miles east and then 3 miles north. What is the magnitude of the net displacement?

Accepted Answer

$$\sqrt{4^2$ + 3^2$} = 5$$ miles

Question 15

Which of the following best describes the role of unit vectors in vector decomposition?

Accepted Answer

Unit vectors define the direction of the axes and allow vectors to be written in component form.

Question 16

A vector $$\vec{D}$$ has components $$D_x = -4 cm $$and $$D_y = 2 cm. $$What is the direction angle $$\phi$$ measured from the positive x-axis?

Accepted Answer

$$\phi = \arctan\left(\frac{2}{-4}\right)$$

Question 17

Which of the following is a scalar quantity?

Accepted Answer

Temperature

Question 18

If $$\vec{A} = 3\hat{i} - 2\hat{j}$$, what is the magnitude of $$\vec{A}$$?

Accepted Answer

$$\sqrt{3^2$ + (-2)^2$} = \sqrt{9 + 4} = \sqrt{13}$$

Question 19

A GPS uses satellite signals to find your position in the earth’s coordinate system. Which concept from Chapter 3 does this illustrate?

Accepted Answer

Coordinate systems

Question 20

If a vector $$\vec{E} is $$decomposed into $$E_x$$ and $$E_y$$, and $$E_x = 0$$, $$E_y = -5$$, what is the direction of $$\vec{E}$$?

Accepted Answer

Downward along the negative y-axis

Vectors and Coordinate Systems: Study Notes

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