Question 1

A vector $$\vec{A}$$ has components $$A_x = 3.20\ \mathrm{m}$$ and $$A_y = -0.800\ \mathrm{m}. $$What is the angle $$	heta (in $$degrees) that $$\vec{A}$$ makes with the $$+x-$$axis, measured counterclockwise from that axis?

Accepted Answer

$$	heta = 346^\circ$$

Question 2

Given a vector $$\vec{A}$$ with $$A_x = -3.00\ \mathrm{m}$$ and $$A_y = 2.10\ \mathrm{m}$$, what is the angle $$	heta (in $$degrees) it makes with the $$+x-$$axis, measured counterclockwise?

Accepted Answer

$$	heta = 35.0^\circ$$

Question 3

A vector $$\vec{A}$$ has $$A_x = -4.70\ \mathrm{m}$$ and $$A_y = 0.900\ \mathrm{m}. $$What is the angle $$	heta (in $$degrees) it makes with the $$+x-$$axis?

Accepted Answer

$$	heta = 169^\circ$$

Question 4

A vector $$\vec{A} is in $$the direction $$39.0^\circ$$ clockwise from the $$y-$$axis. Its $$z-$$component is $$A_z = +12.0\ \mathrm{m}. $$What is the $$y-$$component $$A_y of$$ $$\vec{A}$$?

Accepted Answer

$$A_y = -14.8\ \mathrm{m}$$

Question 5

Given $$\vec{A} = 4.8\hat{i} + 5.7\hat{j}$$, what are the $$x$$ and $$y$$ components of $$\vec{A}$$?

Accepted Answer

$$A_x = 4.8,\ A_y = 5.7$$

Question 6

If $$\vec{A} = 12.2\hat{j} - 4.91\hat{i}$$, what are the $$x$$ and $$y$$ components of $$\vec{A}$$?

Accepted Answer

$$A_x = -4.91,\ A_y = 12.2$$

Question 7

Given $$\vec{A} = -12.0\hat{i} + 22.4\hat{j}$$, what are the $$x$$ and $$y$$ components of $$\vec{A}$$?

Accepted Answer

$$A_x = -12.0,\ A_y = 22.4$$

Question 8

If $$\vec{A} = 5.0\vec{B}$$, where $$\vec{B} = \hat{i} - 6\hat{j}$$, what are the $$x$$ and $$y$$ components of $$\vec{A}$$?

Accepted Answer

$$A_x = 5.0,\ A_y = -30.0$$

Question 9

Given two vectors $$\vec{A} = -3.0\hat{i} + 6.0\hat{j}$$ and $$\vec{B} = 6.0\hat{i} + 2.0\hat{j}$$, what is the angle $$	heta_A (in $$degrees) that $$\vec{A}$$ makes with the $$+x-$$axis?

Accepted Answer

$$	heta_A = 117^\circ$$

Question 10

For the same vectors as above, $$\vec{B} = 6.0\hat{i} + 2.0\hat{j}$$, what is the angle $$	heta_B (in $$degrees) that $$\vec{B}$$ makes with the $$+x-$$axis?

Accepted Answer

$$	heta_B = 18.4^\circ$$

Question 11

If $$\vec{C} = \vec{A} + \vec{B}$$, where $$\vec{A} = -3.0\hat{i} + 6.0\hat{j}$$ and $$\vec{B} = 6.0\hat{i} + 2.0\hat{j}$$, what is the angle $$	heta_C (in $$degrees) that $$\vec{C}$$ makes with the $$+x-$$axis?

Accepted Answer

$$	heta_C = 69.4^\circ$$

Question 12

Given $$\vec{A} \cdot \vec{B} = 7.83$$ and $$\vec{A} = -3.0\hat{i} + 6.0\hat{j}$$, $$\vec{B} = 6.0\hat{i} + 2.0\hat{j}$$, what is the angle $$	heta (in $$degrees) between $$\vec{A}$$ and $$\vec{B}$$?

Accepted Answer

$$	heta = 80.2^\circ$$

Question 13

A plane leaves an airport and flies $$140\ \mathrm{km} at$$ $$64.0^\circ$$ east of north, then changes direction to fly $$230\ \mathrm{km} at$$ $$42.0^\circ$$ south of east. What is the magnitude of the displacement from the airport to the final landing point?

Accepted Answer

$$R = 311\ \mathrm{km}$$

Question 14

Vectors $$\vec{A}$$ and $$\vec{B}$$ have a scalar product $$-6.00$$ and their vector product has magnitude $$9.00. $$What is the angle between these two vectors?

Accepted Answer

$$	heta = 124^\circ$$

Question 15

Two vectors $$\vec{A}$$ and $$\vec{B}$$ have magnitudes $$A = 3.05$$ and $$B = 2.99. $$Their vector product is $$\vec{A} 	imes \vec{B} = -5.09\hat{k} + 2.03\hat{i}. $$What is the angle between $$\vec{A}$$ and $$\vec{B}$$?

Accepted Answer

$$	heta = 36.9^\circ$$

Question 16

A vector $$\vec{A}$$ has $$A_x = 0$$ and $$A_y = 5.0. $$What is the direction of $$\vec{A}$$ relative to the $$+x-$$axis?

Accepted Answer

$$90^\circ$$

Question 17

If $$\vec{A} = 3.0\hat{i} - 4.0\hat{j}$$, what is the magnitude of $$\vec{A}$$?

Accepted Answer

$$5.0$$

Vectors and Their Applications in Physics: Study Notes

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