The vector productEdexcel International A Level Further Maths: Mind map

Exam questions on The vector product

1. The vectors $\mathbf{a}=2\mathbf{i}+\mathbf{j}-\mathbf{k}$ and $\mathbf{b}=\mathbf{i}+3\mathbf{j}+2\mathbf{k}$ are given.
   Find the area of the triangle with sides $\mathbf{a}$ and $\mathbf{b}$, and write down a vector perpendicular to both $\mathbf{a}$ and $\mathbf{b}$ with magnitude $1$.2 marks
2. A parallelepiped has edges represented by the vectors $\mathbf{a}=\mathbf{i}+\mathbf{j}+2\mathbf{k}$, $\mathbf{b}=3\mathbf{i}+\mathbf{j}$ and $\mathbf{c}=2\mathbf{j}+\mathbf{k}$.
   The vector $\mathbf{d}=2\mathbf{j}+\lambda\mathbf{k}$ is such that $\mathbf{a}$, $\mathbf{b}$ and $\mathbf{d}$ lie in the same plane. Find the value of $\lambda$.2 marks
3. The points $P$, $Q$, $R$ and $S$ have coordinates $(1,2,0)$, $(3,3,2)$, $(2,5,1)$ and $(0,1,4)$ respectively.
   Find the exact area of triangle $PQR$.3 marks