If B={v1,v2}B = \{\mathbf{v}_1, \mathbf{v}_2\}B={v1,v2} is a basis for VVV, any vector v∈V\mathbf{v} \in Vv∈V can be written as:
c1v1+c2v2c_1\mathbf{v}_1 + c_2\mathbf{v}_2c1v1+c2v2
c1v1⋅c2v2c_1\mathbf{v}_1 \cdot c_2\mathbf{v}_2c1v1⋅c2v2
Only v1\mathbf{v}_1v1 or v2\mathbf{v}_2v2
c1v1×c2v2c_1\mathbf{v}_1 \times c_2\mathbf{v}_2c1v1×c2v2