Q: Which operation is used to find the angle $$\theta$$ between two vectors $$\vec{A}$$ and $$\vec{B}$$ using their components?

$$\theta = \arccos\left(\frac{\vec{A} \cdot \vec{B}}{|\vec{A}||\vec{B}|}\right)$$

Q: Which of the following is the correct vector product (cross product) of $$\vec{A} = 2\hat{i} + 3\hat{j}$$ and $$\vec{B} = \hat{i} + 4\hat{j}$$?

$$(2 \times 4 - 3 \times 1)\hat{k} = 5\hat{k}$$

Q: A vector $$\vec{A}$$ has components $$A_x = -3$$, $$A_y = 5. $$What is the direction of $$\vec{A}$$ measured from the positive x-axis?

$$\theta = \arctan\left(\frac{5}{-3}\right)$$

Question 1

Which of the following is a fundamental SI unit?

Accepted Answer

Kelvin (K)

Question 2

A scientist measures the mass of a grain of salt as $$2.0 	imes 10$$^{-4}$$ kg. Which SI prefix best describes this mass?

Accepted Answer

Milli-

Question 3

A runner completes a 10-minute walk. What is the distance in meters if the average speed is $$1.2 m/s$$?

Accepted Answer

$$720 m$$

Question 4

Which of the following quantities is a vector?

Accepted Answer

Displacement

Question 5

A measurement is recorded as $$0.02340 m. $$How many significant figures does this value have?

Accepted Answer

4

Question 6

A car travels $$60$$ miles per hour. Convert this speed to meters per second ($$1$$ mile $$= 1609 m).$$

Accepted Answer

$$26.8 m/s$$

Question 7

Which of the following is NOT a correct rule for significant figures?

Accepted Answer

Leading zeros in a number with a decimal are significant.

Question 8

A vector $$\vec{A}$$ has components $$A_x = 3$$ and $$A_y = 4. $$What is the magnitude of $$\vec{A}$$?

Accepted Answer

$$5$$

Question 9

Which operation is used to find the angle $$	heta$$ between two vectors $$\vec{A}$$ and $$\vec{B}$$ using their components?

Accepted Answer

$$	heta = \arccos\left(\frac{\vec{A} \cdot \vec{B}}{|\vec{A}||\vec{B}|}ight)$$

Question 10

A vector $$\vec{A} is $$multiplied by a negative scalar $$-3. $$What happens to $$\vec{A}$$?

Accepted Answer

Its magnitude triples and its direction reverses.

Question 11

Which of the following is dimensionally consistent?

Accepted Answer

$$v = d/t$$

Question 12

A force $$\vec{F} of$$ $$10 N $$acts at a point $$2 m $$from the axis of rotation. What is the magnitude of the torque $$	au$$ produced?

Accepted Answer

$$20 N$$\cdot m$

Question 13

Which of the following is the correct vector product (cross product) of $$\vec{A} = 2\hat{i} + 3\hat{j}$$ and $$\vec{B} = \hat{i} + 4\hat{j}$$?

Accepted Answer

$$(2 	imes 4 - 3 	imes 1)\hat{k} = 5\hat{k}$$

Question 14

A student measures the length of a table as $$1.250 m. $$How many significant figures are in this measurement?

Accepted Answer

4

Question 15

Which of the following is a correct statement about the scalar (dot) product?

Accepted Answer

It is zero if the vectors are perpendicular.

Question 16

A vector $$\vec{A}$$ has components $$A_x = -3$$, $$A_y = 5. $$What is the direction of $$\vec{A}$$ measured from the positive x-axis?

Accepted Answer

$$	heta = \arctan\left(\frac{5}{-3}ight)$$

Question 17

Which of the following is the correct dimensional formula for energy?

Accepted Answer

$$ML^2T$$^{-2}$

Question 18

A vector $$\vec{A} is $$described as $$4.00\hat{i} + 7.00\hat{j}$$ and $$\vec{B} as$$ $$5.00\hat{i} - 2.00\hat{j}. $$What is the magnitude of $$\vec{A} - \vec{B}$$?

Accepted Answer

$$\sqrt{(-1.00)^2$ + (9.00)^2$} = 9.06$$

Question 19

Which of the following is true about the cross product $$\vec{A} 	imes \vec{B}$$?

Accepted Answer

It is a vector perpendicular to both $$\vec{A}$$ and $$\vec{B}.$$

Units, Physical Quantities, and Vectors – Foundations of Physics

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