Podcast
Questions and Answers
What is the formula to find the magnitude of a vector in 3D space?
What is the formula to find the magnitude of a vector in 3D space?
- |v| = x - y - z
- |v| = x + y + z
- |v| = √(x² - y² - z²)
- |v| = √(x² + y² + z²) (correct)
What is the dot product of two perpendicular vectors?
What is the dot product of two perpendicular vectors?
- 0 (correct)
- 2
- 1
- Undefined
In 3D space, what does the cross product of two vectors produce?
In 3D space, what does the cross product of two vectors produce?
- A scalar quantity
- A vector in the direction of the second vector
- A vector perpendicular to both the original vectors (correct)
- A vector in the direction of the first vector
In 3D space, what is the angle between two vectors if their dot product is zero?
In 3D space, what is the angle between two vectors if their dot product is zero?
If a vector's components are (3, 4, 5), what is its magnitude?
If a vector's components are (3, 4, 5), what is its magnitude?
What is the result of the cross product of two parallel vectors in 3D space?
What is the result of the cross product of two parallel vectors in 3D space?
Flashcards
Magnitude of a vector in 3D space
Magnitude of a vector in 3D space
The length of a vector in 3D space, calculated using the Pythagorean theorem in three dimensions.
Dot product of perpendicular vectors
Dot product of perpendicular vectors
The dot product of two perpendicular vectors is always zero.
Cross product of vectors in 3D space
Cross product of vectors in 3D space
A vector perpendicular to both of the original vectors, following the right-hand rule.
Angle between vectors with zero dot product
Angle between vectors with zero dot product
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Magnitude of a vector (3, 4, 5)
Magnitude of a vector (3, 4, 5)
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Cross product of parallel vectors
Cross product of parallel vectors
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Study Notes
Vector Magnitude and Operations in 3D Space
- The magnitude of a vector in 3D space is calculated using the formula: √(x² + y² + z²)
- The dot product of two perpendicular vectors is zero
- The cross product of two vectors in 3D space produces a vector that is perpendicular to both of the original vectors
- If the dot product of two vectors is zero, the angle between them is 90 degrees (perpendicular)
- The magnitude of a vector with components (3, 4, 5) is √(3² + 4² + 5²) = √(9 + 16 + 25) = √50
- The cross product of two parallel vectors in 3D space results in a zero vector
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