Parallel and perpendicular lines (HSC SSCE Mathematics Extension 2): Flashcards
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What is a 3D vector in mathematics?
What is a 3D vector in mathematics?
A vector in 3D space, written as (x, y, z).
How is a direction vector defined in 3D?
How is a direction vector defined in 3D?
It shows the line's direction, e.g., (a, b, c).
What does a parametric equation describe?
What does a parametric equation describe?
Coordinates (x, y, z) as functions of parameter t.
What is the general form of a 3D line equation?
What is the general form of a 3D line equation?
r(t) = r0 + t * d, where r0 is a known point.
How to determine if lines are parallel?
How to determine if lines are parallel?
Their direction vectors are multiples of each other.
What indicates perpendicular lines in 3D?
What indicates perpendicular lines in 3D?
The dot product of their direction vectors is zero.
What are skew lines?
What are skew lines?
Lines that are neither parallel nor intersecting.
How to check if two lines are skew?
How to check if two lines are skew?
They are not parallel and do not intersect.
What software can help visualize 3D lines?
What software can help visualize 3D lines?
GeoGebra and MATLAB are useful for plotting.
Why are these 3D concepts important?
Why are these 3D concepts important?
They apply to real-world scenarios like navigation.