$$\theta = \tan$$^{-1}$$\left(\frac{A_y}{A_x}\right)$$

$$A_x = A \cos \theta$$, $$A_y = A \sin \theta$$

$$\theta = \tan$$^{-1}$$\left(\frac{8}{-6}\right)$$

Question 1

Which of the following best defines a vector?

Accepted Answer

A quantity having both size and direction.

Question 2

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

Accepted Answer

$$5\ 	ext{miles}$$

Question 3

Which of the following is NOT a vector quantity?

Accepted Answer

Temperature

Question 4

If vector $$\vec{A}$$ has components $$A_x = 3$$ and $$A_y = 4$$, what is the magnitude of $$\vec{A}$$?

Accepted Answer

$$5$$

Question 5

Which statement about unit vectors is correct?

Accepted Answer

Unit vectors have magnitude 1 and no units.

Question 6

A bird flies 100 m due east, then 50 m northwest ($$45^\circ$$ north of west). What is the magnitude of the bird’s net displacement?

Accepted Answer

$$74\ 	ext{m}$$

Question 7

Which mathematical operation is used to find the direction $$	heta of a $$vector with components $$A_x$$ and $$A_y$$?

Accepted Answer

$$	heta = 	an$$^{-1}$$\left(\frac{A_y}{A_x}ight)$$

Question 8

Which of the following is true about vector addition?

Accepted Answer

Vectors are added tip-to-tail, and the order of addition does not matter.

Question 9

Given $$\vec{A} = 4\hat{i} + 3\hat{j}$$ and $$\vec{B} = -2\hat{i} + 5\hat{j}$$, what is $$\vec{A} + \vec{B}$$?

Accepted Answer

$$2\hat{i} + 8\hat{j}$$

Question 10

A GPS uses which of the following to determine your position?

Accepted Answer

A coordinate system fixed to the Earth

Question 11

If $$\vec{B} is $$subtracted from $$\vec{A}$$, how is this written in vector notation?

Accepted Answer

$$\vec{A} - \vec{B} = \vec{A} + (-\vec{B})$$

Question 12

Which of the following is a correct statement about the equality of vectors?

Accepted Answer

Two vectors are equal if they have the same magnitude and direction, regardless of their starting points.

Question 13

A vector $$\vec{A}$$ makes an angle $$	heta$$ with the x-axis. What are its components?

Accepted Answer

$$A_x = A \cos 	heta$$, $$A_y = A \sin 	heta$$

Question 14

Which of the following best describes the parallelogram rule for vector addition?

Accepted Answer

The sum of two vectors is the diagonal of the parallelogram formed by the vectors.

Question 15

A vector $$\vec{C}$$ has components $$C_x = -6$$ and $$C_y = 8. $$What is the direction of $$\vec{C}$$ relative to the positive x-axis?

Accepted Answer

$$	heta = 	an$$^{-1}$$\left(\frac{8}{-6}ight)$$

Question 16

Which of the following is a correct statement about multiplying a vector by a scalar?

Accepted Answer

Multiplying a vector by a scalar multiplies all of its components by that scalar.

Question 17

A hiker moves along four displacement vectors: $$\vec{D}_1$$, $$\vec{D}_2$$, $$\vec{D}_3$$, and $$\vec{D}_4. $$What is the net displacement?

Accepted Answer

$$\vec{D}_{net} = \vec{D}_1 + \vec{D}_2 + \vec{D}_3 + \vec{D}_4$$

Question 18

Which of the following is true about the components of a vector?

Accepted Answer

The components are the projections of the vector along the coordinate axes.

Chapter 3: Vectors and Coordinate Systems – Study Notes

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