Q: If two vectors $$A$$ and $$B$$ are not perpendicular, which method can be used to find the magnitude of their resultant vector?

Use the law of cosines: $$R = \sqrt{A^2$ + B^2$ + 2AB \cos \theta}$$

Q: Which trigonometric ratio is used to find the angle $$\theta of a $$vector given its components $$A_x$$ and $$A_y$$?

$$\tan \theta = \frac{A_y}{A_x}$$

Question 1

Which of the following statements best describes a vector?

Accepted Answer

A quantity that has both magnitude and direction.

Question 2

A car drives 90 km due east and then 200 km due east. What is the magnitude of the resultant displacement vector?

Accepted Answer

$$290\ \mathrm{km}$$

Question 3

A person walks 125 m due north and then 85 m due south. What is the magnitude and direction of the resultant displacement?

Accepted Answer

$$40\ \mathrm{m}$$, north

Question 4

An airplane flies 300 km due east and then 700 km due north. What is the magnitude of the resultant displacement?

Accepted Answer

$$762\ \mathrm{km}$$

Question 5

Which equation correctly calculates the magnitude of the resultant vector $$R$$ when two perpendicular vectors $$A$$ and $$B$$ are added?

Accepted Answer

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

Question 6

If a vector makes an angle $$	heta$$ with the horizontal, what is the correct expression for its vertical component?

Accepted Answer

$$A_y = A \sin 	heta$$

Question 7

A runner travels 145 m in a direction $$20.0^\circ$$ north of east, then 155 m in a direction $$35.0^\circ$$ south of east. What is the first step to find the magnitude and direction of the resultant displacement?

Accepted Answer

Resolve each displacement into its x and y components.

Question 8

Which of the following best describes the 'head-to-tail' method of vector addition?

Accepted Answer

Placing the tail of the second vector at the head of the first vector.

Question 9

A vector is described as '30° east of north.' Which direction does this vector point?

Accepted Answer

30° clockwise from north towards east.

Question 10

Given a vector $$A$$ with magnitude $$A$$ and direction $$	heta$$ measured from the x-axis, what is the correct formula for its horizontal (x) component?

Accepted Answer

$$A_x = A \cos 	heta$$

Question 11

A force vector $$\vec{F} is $$applied at an angle $$	heta$$ above the horizontal. Which equation gives the vertical component of the force?

Accepted Answer

$$F_y = F \sin 	heta$$

Question 12

If two vectors $$A$$ and $$B$$ are not perpendicular, which method can be used to find the magnitude of their resultant vector?

Accepted Answer

Use the law of cosines: $$R = \sqrt{A^2$ + B^2$ + 2AB \cos 	heta}$$

Question 13

Which of the following is NOT a vector quantity?

Accepted Answer

Speed

Question 14

A vector has components $$A_x = 3$$ and $$A_y = 4. $$What is its magnitude?

Accepted Answer

$$5$$

Question 15

A vector points $$45^\circ$$ south of east. Which of the following correctly describes its orientation?

Accepted Answer

45° below the east axis towards the south.

Question 16

A person walks 100 m east, then 100 m north. What is the magnitude of the resultant displacement?

Accepted Answer

$$\sqrt{100^2$ + 100^2$} = 141\ \mathrm{m}$$

Question 17

Which trigonometric ratio is used to find the angle $$	heta of a $$vector given its components $$A_x$$ and $$A_y$$?

Accepted Answer

$$	an 	heta = \frac{A_y}{A_x}$$

Question 18

A vector $$A$$ has a magnitude of $$10$$ units and points $$60^\circ$$ north of east. What is its northward (y) component?

Accepted Answer

$$10 \sin 60^\circ = 8.66$$

Question 19

Which of the following is the correct way to add two vectors that are not aligned along the same axis?

Accepted Answer

Resolve each vector into components, add the components, then recombine.

Vectors: Concepts, Addition, and Applications in Physics

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