Quick questions on Scalar and vector products explained: H2 Further Mathematics

The component of $\mathbf{a}$ in the direction of a unit vector $\hat{\mathbf{b}}$ is the scalar projection $\mathbf{a}\cdot\hat{\mathbf{b}}$. This is the basis of resolving a vector along a direction.

The scalar triple product $\mathbf{a}\cdot(\mathbf{b}\times\mathbf{c})$ is a number equal to the determinant of the matrix with rows $\mathbf{a}, \mathbf{b}, \mathbf{c}$. Its absolute value is the volume of the parallelepiped spanned by the three vectors, and the volume is zero exactly when the three vectors are coplanar (linearly dependent).

$\mathbf{a}\times\mathbf{b} = -\mathbf{b}\times\mathbf{a}$; the determinant's middle term carries a minus sign.

State the condition on the scalar product for two non-zero vectors to be perpendicular. [1 mark]

What does $|\mathbf{a}\times\mathbf{b}|$ represent geometrically? [1 mark]

Three vectors have scalar triple product $0$. What does this mean? [1 mark]