Q: If a vector $$\vec{v}$$ has components $$\langle x, y \rangle$$, what is the formula for its direction angle $$\theta$$ measured from the positive x-axis?

$$\theta = \tan$$^{-1}$$ \left( \frac{y}{x} \right)$$

Q: A vector $$\vec{v}$$ has components $$\langle -21.6, 46.2 \rangle. $$What is the direction angle $$\theta (in $$degrees) from the positive x-axis?

$$\theta = \tan$$^{-1}$$ \left( \frac{46.2}{-21.6} \right)$$

Question 1

Which of the following best describes a vector?

Accepted Answer

A quantity with both direction and magnitude

Question 2

Given a vector with a magnitude of $$50$$ units at an angle of $$65^\circ$$ above the positive x-axis, what are its x and y components to the nearest tenth?

Accepted Answer

$$\langle 21.1, 46.2 \rangle$$

Question 3

What is the magnitude of the vector $$\langle -24, 7 \rangle$$?

Accepted Answer

$$\sqrt{24^2$ + 7^2$}$$

Question 4

A plane travels $$47.17 km at$$ $$32.005^\circ$$ south of west. What are the x and y components of its displacement?

Accepted Answer

$$\langle -40, -25 \rangle$$

Question 5

Which of the following is the correct way to multiply the vector $$\langle 3, 2 \rangle by a $$scalar $$k = 4$$?

Accepted Answer

$$\langle 12, 8 \rangle$$

Question 6

If a vector is described as $$35^\circ$$ east of north, which direction does it point?

Accepted Answer

35 degrees clockwise from north towards east

Question 7

Given vectors $$\langle 4, 1 \rangle$$ and $$\langle -3, 2 \rangle$$, what is their sum?

Accepted Answer

$$\langle 1, 3 \rangle$$

Question 8

A ferry is traveling at $$20 mi/h$$, $$15.64^\circ$$ north of west. What is the northward component of its velocity?

Accepted Answer

$$20 \sin 15.64^\circ$$

Question 9

Which of the following statements about the magnitude of a vector is correct?

Accepted Answer

Magnitude is always zero or positive

Question 10

If a vector $$\vec{v}$$ has components $$\langle x, y angle$$, what is the formula for its direction angle $$	heta$$ measured from the positive x-axis?

Accepted Answer

$$	heta = 	an$$^{-1}$$ \left( \frac{y}{x} ight)$$

Question 11

A vector is described as $$60^\circ$$ north of west. Which of the following best describes its orientation?

Accepted Answer

60 degrees counterclockwise from west towards north

Question 12

Which of the following is a scalar quantity?

Accepted Answer

Speed

Question 13

If you add the vectors $$\langle 2, 5 \rangle$$ and $$\langle -4, 3 \rangle$$, what is the resultant vector?

Accepted Answer

$$\langle -2, 8 \rangle$$

Question 14

A vector $$\vec{a}$$ has components $$\langle 6, -8 \rangle. $$What is its magnitude?

Accepted Answer

$$\sqrt{6^2$ + (-8)^2$}$$

Question 15

Which of the following best describes the resultant vector?

Accepted Answer

The sum of two or more vectors

Question 16

If a vector $$\vec{v} is $$multiplied by a scalar $$-2$$, what happens to its direction and magnitude?

Accepted Answer

The magnitude is doubled and the direction is reversed

Question 17

A vector from the origin to the point $$(x, y)$$ can be written as:

Accepted Answer

$$\langle x, y \rangle$$

Question 18

Which of the following is NOT a correct way to describe the direction of a vector?

Accepted Answer

Magnitude

Question 19

A vector $$\vec{v}$$ has components $$\langle -21.6, 46.2 angle. $$What is the direction angle $$	heta (in $$degrees) from the positive x-axis?

Accepted Answer

$$	heta = 	an$$^{-1}$$ \left( \frac{46.2}{-21.6} ight)$$

Vectors in Trigonometry: Definitions, Operations, and Applications

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