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Kendrick Pierce 2022-05-22 Answered
The equation d = | A x + B y + C z + D | ( A 2 + B 2 + C 2 ) gives is the distance between a plane and a point as the value 'd'. What is the unit of this value? Why is the distance between the plane and the point not a vector?
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Answers (2)

Haleigh Vega
Answered 2022-05-23 Author has 13 answers
The equation d = | A x + B y + C z + D | A 2 + B 2 + C 2 gives us the distance a point from a plane in R 3 . Here we discuss about Euclidean space and distances measured by physical units, here obey on x, y and z and A, B, C and D are constant scalars belong to R 3 without units. Then the unit of d is the same as variables have.
Also, the distance is not a vector, it is the smallest way between the point and a point on plane measured without direction.
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Briana Petty
Answered 2022-05-24 Author has 3 answers
Distances have units of length. You can see this from the formula, where the numerator has units like A x and the denominator has units like A, so the ratio has units of x. You can certainly define a vector from the point to the nearest point on the plane, but that is not this formula. This formula gives the magnitude of that vector.
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