Q: Which formula gives the magnitude of the vector product (cross product) of two vectors $$\vec{A}$$ and $$\vec{B}$$ separated by angle $$\theta$$?

$$|\vec{A} \times \vec{B}| = AB \sin \theta$$

Question 1

Vector A points in the $$+z$$ direction, and vector B makes an angle $$	heta$$ with the $$+z$$ axis toward the $$+y$$ axis in the $$yz-$$plane. For which value of $$	heta$$ does the scalar product $$\vec{A} \cdot \vec{B}$$ reach its maximum magnitude?

Accepted Answer

$$	heta = 0^\circ$$

Question 2

Given vectors $$\vec{A} in $$the $$+z$$ direction and $$\vec{B} at an $$angle $$	heta$$ from the $$+z$$ axis toward the $$+y$$ axis, for which value of $$	heta$$ does the vector product $$\vec{A} 	imes \vec{B}$$ have its maximum magnitude?

Accepted Answer

$$	heta = 90^\circ$$

Question 3

If $$\vec{A}$$ has magnitude $$A$$ and points in the $$+z$$ direction, and $$\vec{B}$$ has magnitude $$B$$ and is at an angle $$	heta$$ from the $$+z$$ axis toward $$+y$$, what is the magnitude of the scalar product $$\vec{A} \cdot \vec{B}$$?

Accepted Answer

$$AB \cos 	heta$$

Question 4

A car travels along a straight line with a displacement of $$120\ \mathrm{m} in$$ $$8\ \mathrm{s}. $$What is its average velocity?

Accepted Answer

$$15\ \mathrm{m/s}$$

Question 5

Which of the following best describes instantaneous velocity?

Accepted Answer

The velocity of an object at a specific instant in time.

Question 6

If a runner moves from point A to point B in a straight line, covering $$50\ \mathrm{m} in$$ $$10\ \mathrm{s}$$, then immediately returns to point A in $$15\ \mathrm{s}$$, what is the runner's average velocity for the entire trip?

Accepted Answer

$$0\ \mathrm{m/s}$$

Question 7

A cyclist starts from rest and accelerates uniformly along a straight path. If the cyclist covers $$100\ \mathrm{m} in$$ $$20\ \mathrm{s}$$, what is the average velocity?

Accepted Answer

$$5\ \mathrm{m/s}$$

Question 8

Which equation correctly relates displacement $$\Delta x$$, average velocity $$v_{avg}$$, and time interval $$\Delta t$$?

Accepted Answer

$$\Delta x = v_{avg} \Delta t$$

Question 9

A ball is thrown straight up and returns to its starting point after $$4\ \mathrm{s}. $$What is its average velocity during this time?

Accepted Answer

$$0\ \mathrm{m/s}$$

Question 10

If vector $$\vec{A} is in $$the $$+z$$ direction and vector $$\vec{B} is at$$ $$90^\circ$$ from the $$+z$$ axis toward $$+y$$, what is the direction of $$\vec{A} 	imes \vec{B}$$?

Accepted Answer

$$-x$$ direction

Question 11

A student walks $$30\ \mathrm{m}$$ east, then $$40\ \mathrm{m}$$ north. What is the magnitude of the displacement?

Accepted Answer

$$50\ \mathrm{m}$$

Question 12

Which of the following statements about the scalar product (dot product) of two vectors is correct?

Accepted Answer

It is maximum when the vectors are parallel.

Question 13

A car moves along a straight road with a constant velocity of $$20\ \mathrm{m/s}$$ for $$5\ \mathrm{s}. $$What is its displacement?

Accepted Answer

$$100\ \mathrm{m}$$

Question 14

If the angle between two vectors is $$0^\circ$$, what is the value of their vector product?

Accepted Answer

$$0$$

Question 15

A train travels $$200\ \mathrm{km}$$ north in $$4\ \mathrm{h}$$, then $$150\ \mathrm{km}$$ east in $$3\ \mathrm{h}. $$What is the average velocity magnitude for the entire trip?

Accepted Answer

$$50\ \mathrm{km/h}$$

Question 16

Which of the following is NOT a vector quantity?

Accepted Answer

Time

Question 17

A person walks $$60\ \mathrm{m}$$ west, then $$80\ \mathrm{m}$$ south. What is the magnitude of the displacement?

Accepted Answer

$$100\ \mathrm{m}$$

Question 18

If the displacement of an object is zero after a certain time interval, what can be said about its average velocity?

Accepted Answer

The average velocity is zero.

Question 19

Which formula gives the magnitude of the vector product (cross product) of two vectors $$\vec{A}$$ and $$\vec{B}$$ separated by angle $$	heta$$?

Accepted Answer

$$|\vec{A} 	imes \vec{B}| = AB \sin 	heta$$

Vectors and Motion Along a Straight Line: Study Notes for College Physics

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