Which of the following statements are true?

I: For every plane, there is an infinite number of equations in the form \(ax + by + cz + d = 0\) to represent the same plane but in all of these equations, \( a, b, c, d \) all remain in the same proportions to each other.

II: For every plane, there is an infinite number of equations in the form \( \vec{n} \cdot (\vec{v} - \vec{v_0}) = 0 \) to represent the same plane, where \( \vec{n} \) is the normal vector to the plane and \( \vec{v} - \vec{v_0} \) is a vector in the plane.

III: The same plane can have multiple equations, but only by the method of changing the norm (magnitude/length/absolute value) of the normal vector to the plane.

×

Problem Loading...

Note Loading...

Set Loading...