Volume of parallelepiped defined by vectors \begin{align} \begin{bmatrix}a\\b\\c\end{bmatrix}&,\quad \begin{bmatrix}v_1\\v_2\\v_3\end{bmatrix},\quad\begin{bmatrix}w_1\\w_2\\w_3\end{bmatrix} = \det\begin{pmatrix}\begin{bmatrix}a&v_1&w_1\\b&v_2&w_2\\c&v_3&w_3\end{bmatrix}\end{pmatrix}\\ &= a(v_2w_3 - v_3w_2) + b(v_3w_1 - v_1w_3) + c(v_1w_2 - v_2w_1)\\ &= a(\text{Area of parallelogram obtained by projecting parallelepiped on the $yz$ plane})\\ &+b(\text{Area of parallelogram obtained by projecting parallelepiped on the $zx$ plane}) \\ &+c(\text{Area of parallelogram obtained by projecting parallelepiped on the $xy$ plane}) \end{align}

I can visualize the case when any one component of vectors $v$ and $w$ are $0$. Suppose the $z$ component is $0$. So there would not be any parallelogram formed on the $yz$ and $zx$ plane. So the volume would simply be $$=c(\text{Area of parallelogram obtained by projecting parallelepiped on the $xy$ plane})$$ which is simple enough to visualize. But, I am having trouble visualizing when all the three components of $v$ and $w$ are non-zero. Can anyone help?