Vector productAQA A-Level Further Maths: Mind map

Exam questions on Vector product

1. The vectors $\mathbf a=2\mathbf i-\mathbf j+3\mathbf k$ and $\mathbf b=\mathbf i+4\mathbf j-2\mathbf k$ are given.
   Show that $\mathbf a\times\mathbf b$ is perpendicular to $\mathbf b$.2 marks
2. Triangle $ABC$ has vertices $A(1,0,2)$, $B(3,2,3)$ and $C(2,-1,5)$.
   Find the exact perpendicular distance from $C$ to the line $AB$.2 marks
3. The line $l_1$ has equation $(\mathbf r-\mathbf a)\times\mathbf b=\mathbf 0$, where $\mathbf a=\begin{pmatrix}1 \\ 2 \\ -1\end{pmatrix}$ and $\mathbf b=\begin{pmatrix}2 \\ -1 \\ 3\end{pmatrix}$.
   Show that the point $(5,0,5)$ lies on $l_1$.3 marks