Q: If a vector $$\vec{A}$$ has components $$A_x = -4$$ and $$A_y = 3$$, what is the direction angle $$\theta ($$measured counterclockwise from the positive x-axis)?

$$\theta = \tan$$^{-1}$$(3/(-4))$$

Question 1

Which of the following best describes a vector quantity?

Accepted Answer

A quantity that has both magnitude and direction, such as displacement or velocity.

Question 2

Sam walks 200 ft northeast from his house. Bill walks 200 ft northeast from his house, which is at a different location. What can be said about their displacement vectors?

Accepted Answer

Their displacement vectors are the same because displacement depends only on the magnitude and direction, not the starting point.

Question 3

If two vectors $$\vec{A}$$ and $$\vec{B}$$ are at right angles to each other, what is the magnitude of their sum $$\vec{C} = \vec{A} + \vec{B}$$?

Accepted Answer

$$C = \sqrt{A^2$ + B^2$}$$

Question 4

A bird flies 100 m due east and then 50 m northwest (45° north of west). What is the magnitude of the bird's net displacement?

Accepted Answer

$$74\ 	ext{m}$$

Question 5

Which of the following is NOT a vector quantity?

Accepted Answer

Mass

Question 6

Given a vector $$\vec{A}$$ with components $$A_x = 3$$ and $$A_y = 4$$, what is the magnitude $$|\vec{A}|$$?

Accepted Answer

$$|\vec{A}| = 5$$

Question 7

A force of $$720\ 	ext{N} is $$applied at an angle of $$15^\circ to a $$bone. What is the component of this force perpendicular to the bone?

Accepted Answer

$$720 \sin 15^\circ$$

Question 8

Which statement about the addition of vectors is correct?

Accepted Answer

Vectors are added by placing them head-to-tail and finding the resultant vector.

Question 9

If a vector $$\vec{A}$$ has components $$A_x = -4$$ and $$A_y = 3$$, what is the direction angle $$	heta ($$measured counterclockwise from the positive x-axis)?

Accepted Answer

$$	heta = 	an$$^{-1}$$(3/(-4))$$

Question 10

Which of the following best describes the use of unit vectors in component representation?

Accepted Answer

Unit vectors are used to express the direction of a vector along coordinate axes and have magnitude 1.

Question 11

A vector $$\vec{B}$$ has a magnitude of $$10$$ and points $$60^\circ$$ above the x-axis. What are its x- and y-components?

Accepted Answer

$$B_x = 10 \cos 60^\circ$$, $$B_y = 10 \sin 60^\circ$$

Question 12

If you multiply a vector $$\vec{S} by a $$scalar $$c$$, what is the result?

Accepted Answer

A new vector in the same direction as $$\vec{S}$$ with magnitude $$c|\vec{S}|$$

Question 13

Which coordinate system is most commonly used for vector decomposition in introductory physics?

Accepted Answer

Cartesian coordinate system

Question 14

A vector $$\vec{A} is $$decomposed into $$A_x$$ and $$A_y$$ components. Which equation gives the magnitude of $$\vec{A}$$?

Accepted Answer

$$|\vec{A}| = \sqrt{A_x^2$ + A_y^2$}$$

Question 15

In a tilted coordinate system, what remains true about the axes?

Accepted Answer

The axes are still perpendicular but rotated relative to the original axes.

Question 16

A vector $$\vec{D} is $$the sum of three vectors: $$\vec{A}$$, $$\vec{B}$$, and $$\vec{C}. $$Which of the following is the correct component form for $$\vec{D}$$?

Accepted Answer

$$\vec{D} = (A_x + B_x + C_x)\hat{i} + (A_y + B_y + C_y)\hat{j}$$

Question 17

A vector $$\vec{F}$$ has a magnitude of $$8$$ and points $$30^\circ$$ below the positive x-axis. What is the y-component $$F_y$$?

Accepted Answer

$$F_y = -8 \sin 30^\circ$$

Question 18

Which of the following statements about the zero vector is correct?

Accepted Answer

The zero vector has a magnitude of zero and no specific direction.

Question 19

A vector $$\vec{A} is $$represented as $$\vec{A} = 3\hat{i} + 4\hat{j}. $$What is the angle $$	heta it $$makes with the positive x-axis?

Accepted Answer

$$	heta = 	an$$^{-1}$$(4/3)$$

Vectors and Coordinate Systems – Study Notes for Physics 1051

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