Vector Notation in 2D and 3D
This question examines your understanding of vector representation in two and three dimensions. Answer the following parts:
Part b
Consider the 2D vector \(\vec{v} = 3\mathbf{i} + 4\mathbf{j}\) extended into 3D by adding a z-component of 5, resulting in \(\vec{v} = 3\mathbf{i} + 4\mathbf{j} + 5\mathbf{k}\). Express this 3D vector in component form and compute its magnitude.