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Vectors Trivia Quiz

Vectors are critical to both modern-day physics and math. Here's a quick refresher.

A multiple-choice quiz by CellarDoor. Estimated time: 4 mins.

Author
CellarDoor

Time
4 mins

Type
Multiple Choice

Quiz #
43,072

Updated
Dec 03 21

# Qns
10

Difficulty
Average

Avg Score
7 / 10

Plays
3551

One at a Time - Single Page - Timed Game

Question 1 of 10

1. What are the two basic characteristics of a vector? Hint

magnitude and sign (positive or negative)

curvature and sign (positive or negative)

curvature and direction

magnitude and direction

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Question 2 of 10

2. Vectors are often split into two or more orthogonal components. What is true of these components in relation to each other? Hint

They are antiparallel.

They are the same magnitude.

They are perpendicular.

They are the same curvature.

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Question 3 of 10

3. Where 'a' is the length of the vector and 'B' is the angle it makes with the x-axis, what is the length of its component along the x-axis? Hint

a cosB

B cosa

a sinB

a tanB

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Question 4 of 10

4. How are vectors represented graphically? Hint

As straight lines

As oriented curves

As squiggly lines

As arrows

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Question 5 of 10

5. What is a 'unit vector'? Hint

a vector with uniform curvature (like an arc of a circle)

equal to one one-thousandth of a kilovector

a vector in the horizontal direction

a vector with a magnitude of 1

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Question 6 of 10

6. How do you add two vectors graphically? Hint

Place them head-to-tail and draw the addition vector from the head of one to the tail of the other.

Place them head-to-tail and draw the addition vector from the tail of one to the head of the other.

Place them tail-to-tail and draw the addition vector connecting the two heads.

This can't be done; vectors can only be added algebraically.

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Question 7 of 10

7. How do you add two vectors algebraically? Hint

Break the vectors into components. Then add x-components, y-components, etc, algebraically.

This can't be done; vectors can only be added graphically.

Break the vectors into components, then add the lengths of all of them together.

Add each of the characteristics from Q1.

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Question 8 of 10

8. The norm of a vector, found by taking the square root of the sum of the squares of the components, is equal to what quantity? Hint

average component

degree of curvature

magnitude

angle with respect to horizontal

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Question 9 of 10

9. The dot product is used to multiply two vectors for a scalar result. When you dot vectors r and s, with angle Q between them, the answer is equal to which of the following values? Hint

(norm of r) (norm of s) (cosQ)

Qcos((norm of r) (norm of s))

(norm of r) (norm of s) (sinQ)

(norm of r) (norm of s) (tanQ)

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Question 10 of 10

10. The cross product is a way of multiplying two vectors for a result that is a vector. What geometrical quantity does its length represent? Hint

area of the triangle defined by the two vectors

statistical mean of the two vectors

area of the circle sector defined by the two vectors

area of the parallelogram defined by the two vectors

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Oct 31 2024 : Guest 69: 10/10
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Quiz Answer Key and Fun Facts

1. What are the two basic characteristics of a vector?

Answer: magnitude and direction

A scalar quantity, which has only size, is any ordinary number like 13 or -2. A vector would be something like 15 mph going NNE, or 3 in the direction of 85 degrees above the horizontal. The magnitude of a vector is an absolute value: it's never negative.

2. Vectors are often split into two or more orthogonal components. What is true of these components in relation to each other?

Answer: They are perpendicular.

The vector itself can be thought of as the hypotenuse of a right triangle, where the two legs are the components. In Cartesian coordinates, a vector is expressed in terms of its {coordinates;} a size-2 vector in the y-direction would be (0,2) -- 0 directed along the x-axis and 2 directed along the y-axis.

3. Where 'a' is the length of the vector and 'B' is the angle it makes with the x-axis, what is the length of its component along the x-axis?

Answer: a cosB

This comes from basic trigonometry. The length of the component along the y-axis would be a*sinB.

4. How are vectors represented graphically?

Answer: As arrows

This method allows both magnitude (the length of the arrow) and direction to be represented.

5. What is a 'unit vector'?

Answer: a vector with a magnitude of 1

Unit vectors are used to define direction. The three most commonly used are i, j, and k, defining the directions of the x, y, and z axes, respectively.

6. How do you add two vectors graphically?

Answer: Place them head-to-tail and draw the addition vector from the tail of one to the head of the other.

Remember, the direction of the addition vector is as important as its length. The addition of two vectors is equivalent to traveling the vectors consecutively: you eventually reach the same place relative to your starting point.

7. How do you add two vectors algebraically?

Answer: Break the vectors into components. Then add x-components, y-components, etc, algebraically.

This method is also called component addition. Analysis reveals that this method is mathematically equivalent to the graphical method.

8. The norm of a vector, found by taking the square root of the sum of the squares of the components, is equal to what quantity?

Answer: magnitude

The norm of vector r is often indicated by enclosing r in absolute-value signs. A Euclidean norm is found by the method described above - you'll encounter other varieties of norms as you progress in math and physics, but they're all equal to the magnitude.

9. The dot product is used to multiply two vectors for a scalar result. When you dot vectors r and s, with angle Q between them, the answer is equal to which of the following values?

Answer: (norm of r) (norm of s) (cosQ)

Another way to calculate the dot product is by multiplying the x-components by each other, the y-components by each other, and so on -- then you add all the products. It's interesting to note that the dot product of any two perpendicular vectors is zero.

10. The cross product is a way of multiplying two vectors for a result that is a vector. What geometrical quantity does its length represent?

Answer: area of the parallelogram defined by the two vectors

The cross product is defined only in three dimensions and higher, since that vector is always perpendicular to both the original two vectors. So if you drew two vectors on a sheet of paper and took their cross product, the resultant would either rise out of or sink into the page. The magnitude has the value (magnitude of r)(magnitude of s)(sinQ).

Source: Author CellarDoor

This quiz was reviewed by FunTrivia editor rossian before going online.
Any errors found in FunTrivia content are routinely corrected through our feedback system.

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