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?

Question

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 &#039;d&#039;. What is the unit of this value? Why is the distance between the plane and the point not a vector?

Haleigh Vega · Accepted Answer

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.

Briana Petty · Accepted Answer

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.

The equation d = <mrow class="MJX-TeXAtom-ORD"> | </mrow>

Answered question

Answer & Explanation

New Questions in Pre-Algebra