Q: If vector $$\vec{A}$$ has components $$A_x = 8 m $$and $$A_y = 6 m$$, what is the magnitude and direction of $$\vec{A}$$?

Magnitude: $$\sqrt{8^2$ + 6^2$} = 10 m$$, Direction: $$\tan$$^{-1}$$(6/8) = 36.87^\circ$$

Question 1

Which of the following quantities is a vector?

Accepted Answer

Displacement

Question 2

A person walks 3 m east and then 4 m north. What is the magnitude of their total displacement?

Accepted Answer

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

Question 3

If you add two vectors graphically, what method should you use?

Accepted Answer

Place the arrows tip-to-tail

Question 4

A box is pushed with a force of 12 N to the right and an unknown force upward. The total force is 13 N. What is the magnitude of the upward force?

Accepted Answer

$$\sqrt{13^2$ - 12^2$} = 5 N$$

Question 5

Which statement about vector addition is correct?

Accepted Answer

The order of addition does not affect the resultant vector

Question 6

A delivery truck travels 8 miles east, 5 miles north, and 4 miles east again. What is the magnitude of its final displacement from the origin?

Accepted Answer

$$\sqrt{(8+4)^2$ + 5^2$} = \sqrt{144 + 25} = \sqrt{169} = 13$$ miles

Question 7

When subtracting vectors graphically, what must you do to the vector being subtracted?

Accepted Answer

Reverse its direction

Question 8

If vector $$\vec{A}$$ has components $$A_x = 8 m $$and $$A_y = 6 m$$, what is the magnitude and direction of $$\vec{A}$$?

Accepted Answer

Magnitude: $$\sqrt{8^2$ + 6^2$} = 10 m$$, Direction: $$	an$$^{-1}$$(6/8) = 36.87^\circ$$

Question 9

A vector $$\vec{B}$$ has a magnitude of 13 m and makes an angle of $$67.4^\circ$$ with the positive x-axis. What is the x-component $$B_x$$?

Accepted Answer

$$13 \cos(67.4^\circ)$$

Question 10

Which of the following best describes a unit vector?

Accepted Answer

A vector with magnitude 1 pointing in a specific direction

Question 11

Given $$\vec{A} = 4\hat{i} + 2\hat{j}$$ and $$\vec{B} = -\hat{i} + 2\hat{j}$$, what is $$\vec{R} = \vec{A} + \vec{B} in $$unit vector notation?

Accepted Answer

$$3\hat{i} + 4\hat{j}$$

Question 12

A vector $$\vec{F} is 65 m $$long, directed $$30.5^\circ$$ below the positive x-axis. What is the y-component $$F_y$$?

Accepted Answer

$$-65 \sin(30.5^\circ)$$

Question 13

A helicopter travels 225 m at $$53.1^\circ$$ south of east. What is the x-component of its displacement?

Accepted Answer

$$225 \cos(53.1^\circ)$$

Question 14

If $$\vec{A} = (3\hat{i} - 3\hat{j}) m$$, $$\vec{B} = (\hat{i} - 4\hat{j}) m$$, and $$\vec{C} = (-2\hat{i} + 5\hat{j}) m$$, what is the magnitude of $$\vec{D} = \vec{A} + \vec{B} + \vec{C}$$?

Accepted Answer

$$\sqrt{2^2$ + (-2)^2$} = \sqrt{4 + 4} = 2\sqrt{2} m$$

Question 15

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

Accepted Answer

The magnitude changes, but the direction remains the same

Question 16

A vector has components $$A_x = -77 cm $$and $$A_y = 36 cm. $$What is the magnitude of the vector?

Accepted Answer

$$\sqrt{(-77)^2$ + 36^2$} = \sqrt{5929 + 1296} = \sqrt{7225} = 85 cm$$

Question 17

Which direction does the unit vector $$\hat{j}$$ point?

Accepted Answer

Positive y-direction

Vectors and Coordinate Systems: Study Notes

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