Podcast
Questions and Answers
A vector only has magnitude, not direction.
A vector only has magnitude, not direction.
False (B)
Which of the following is true about equal vectors?
Which of the following is true about equal vectors?
- They have the same magnitude and the same direction. (correct)
- They have the same magnitude but different directions.
- They must start at the same point.
- They have different magnitudes but the same direction.
What term describes the length of a vector?
What term describes the length of a vector?
magnitude
A vector with a magnitude of 1 is known as a(n) _____ vector.
A vector with a magnitude of 1 is known as a(n) _____ vector.
What is the purpose of scaling a vector so that its magnitude is 1?
What is the purpose of scaling a vector so that its magnitude is 1?
Match the following:
Match the following:
Consider two vectors with Cartesian components. What operation is performed on corresponding components when adding the vectors?
Consider two vectors with Cartesian components. What operation is performed on corresponding components when adding the vectors?
The Cartesian components i, j, and k are used to describe coordinates in 2D space.
The Cartesian components i, j, and k are used to describe coordinates in 2D space.
The Cartesian components of a vector define the amount of movement in the _, _, and z directions.
The Cartesian components of a vector define the amount of movement in the _, _, and z directions.
If $a = \begin{pmatrix} 3 \ 4 \ 1 \end{pmatrix}$, what is $|a|$?
If $a = \begin{pmatrix} 3 \ 4 \ 1 \end{pmatrix}$, what is $|a|$?
Scalar _______ is the process of multiplying each component of a vector by a scalar value.
Scalar _______ is the process of multiplying each component of a vector by a scalar value.
Given vectors $u = 2i - 3j + k$ and $v = -i + 5j - 2k$, what is $u + v$?
Given vectors $u = 2i - 3j + k$ and $v = -i + 5j - 2k$, what is $u + v$?
To find a unit vector, you divide each component of the vector by its magnitude.
To find a unit vector, you divide each component of the vector by its magnitude.
In the expression $\sqrt{3} \sin x - \cos x = k \sin(x - a)$, the value of k represents the _______ of the resulting sinusoidal function.
In the expression $\sqrt{3} \sin x - \cos x = k \sin(x - a)$, the value of k represents the _______ of the resulting sinusoidal function.
If two vectors are described as components in terms of i, j, and k, what are i, j, and k called?
If two vectors are described as components in terms of i, j, and k, what are i, j, and k called?
Flashcards
What is a vector?
What is a vector?
A quantity with both magnitude and direction.
When are vectors equal?
When are vectors equal?
Vectors that have the same magnitude and direction are considered equal, regardless of their starting point.
What is the magnitude of a vector?
What is the magnitude of a vector?
The length of the vector.
How do you add vectors in component form?
How do you add vectors in component form?
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How do you subtract vectors in component form?
How do you subtract vectors in component form?
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What is a unit vector?
What is a unit vector?
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How to create a unit vector?
How to create a unit vector?
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What are i, j, and k in Cartesian components?
What are i, j, and k in Cartesian components?
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Study Notes
- Vectors are covered in Higher Chapter 5, Lesson 1.
- It is important to understand vector terminology.
- Vectors can be added and subtracted.
- Magnitude of vectors can be found in both 2D and 3D.
- Vectors should be expressed in unit form with correct notation.
- A vector has both size and direction.
- Vectors that are equal have the same magnitude and direction.
- The magnitude of a vector indicates its length.
- To create 'unit' vectors, scale the vector so that its magnitude equals 1.
- Cartesian components describe 3D coordinates using 'some amount of' directions.
- The unit vectors j and k point in certain directions of the 3D coordinate system.
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