Final answer:
To determine for what value an object is in the plane spanned by two vectors, one must resolve the object's position into components that are parallel and perpendicular to the plane. Vector projection and component formulas are used for this purpose.
Step-by-step explanation:
The question seems to be referencing a scenario in which an object's location relative to a plane spanned by two vectors is being considered. To determine for what value an object is in the plane spanned by certain vectors, the components of the object's position vector need to be resolved into components that act perpendicular (w⊥) and parallel (w∥) to the surface of the plane. These components can typically be calculated using vector projection and vector component formulas.
In linear algebra, if we denote the object's position vector by v, and the two vectors spanning the plane as u and w, we can determine whether v is in the plane spanned by u and w by writing v as a linear combination of u and w. If such a combination exists, v lies within the plane. The equation σ = σ0d/2λ also suggests a relationship between the spanning distance and surface tension, indicating that as the spanning distance (d) increases, so does the inward pull (σ), provided surface tension (σ0) and the wavelength (λ) are constants.