Questions and Answers
What is the formula to find the magnitude of a vector in 3D space?
|v| = √(x² + y² + z²)
What is the dot product of two perpendicular vectors?
0
In 3D space, what does the cross product of two vectors produce?
A vector perpendicular to both the original vectors
In 3D space, what is the angle between two vectors if their dot product is zero?
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If a vector's components are (3, 4, 5), what is its magnitude?
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What is the result of the cross product of two parallel vectors in 3D space?
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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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