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linuxux
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Homework Statement
Hello, how to find the distance between two planes when given their cartesian equations?
help appreciated, thanks.
The distance between planes refers to the shortest distance between two parallel planes in a three-dimensional space. It is the length of the line that is perpendicular to both planes and connects them.
The distance between planes can be calculated using the formula d = |ax + by + cz + d|/√(a² + b² + c²), where a, b, and c are the coefficients of the plane's equation in standard form (ax + by + cz + d = 0).
No, the distance between planes is always a positive value. This is because the formula for calculating distance involves taking the absolute value of the expression.
If the distance between planes is 0, then the planes are parallel. If the distance is greater than 0, the planes are considered to be skew (non-parallel) and do not intersect. If the distance is equal to 0, the planes are coincident (they overlap) and have an infinite number of points in common.
No, the distance between planes only determines the relationship of parallelism or skewness. To determine if two planes are perpendicular, we need to check if their normal vectors (vectors perpendicular to the plane) are perpendicular to each other.