Proving Vector Equality in Plane and Space
Consider two vectors \(\vec{u}\) and \(\vec{v}\) defined in Cartesian coordinate systems. Vector \(\vec{u}\) in 2D is given by \(\vec{u} = \begin{pmatrix} a \\ b \end{pmatrix}\) and vector \(\vec{v}\) in 2D is given by \(\vec{v} = \begin{pmatrix} c \\ d \end{pmatrix}\). This question explores the conditions under which these vectors are considered equal in both 2D […]