3D space (HSC SSCE Mathematics Extension 2): Flashcards
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Practise the cards
10 cards from this deck
What are the coordinates for a point in 3D space?
What are the coordinates for a point in 3D space?
Coordinates are given as (x, y, z) in 3D space.
What does the 3D Cartesian system use for axes?
What does the 3D Cartesian system use for axes?
It uses three perpendicular axes: x, y, and z.
How do you determine the coordinates of a point in space?
How do you determine the coordinates of a point in space?
Identify its distances from the axes: (x, y, z).
What is the equation of a plane through point P?
What is the equation of a plane through point P?
The equation is ax + by + cz = d.
How many octants are in 3D space?
How many octants are in 3D space?
There are eight octants in 3D space.
What is the distance formula in 3D space?
What is the distance formula in 3D space?
D = √((x2 - x1)² + (y2 - y1)² + (z2 - z1)²)
What is the basic equation of a sphere?
What is the basic equation of a sphere?
(x-h)² + (y-k)² + (z-l)² = r².
What does the center of a sphere represent?
What does the center of a sphere represent?
The center is the point (h, k, l) in the sphere's equation.
What is the radius in the sphere's equation?
What is the radius in the sphere's equation?
The radius is denoted by r in the sphere's equation.
Name a field that uses 3D space concepts.
Name a field that uses 3D space concepts.
Physics, engineering, and computer graphics use 3D space.