The scalar productEdexcel International A Level Maths: Mind map

Exam questions on The scalar product

1. The vectors $\mathbf{p}=2\mathbf{i}-3\mathbf{j}+\mathbf{k}$ and $\mathbf{q}=4\mathbf{i}+\mathbf{j}-5\mathbf{k}$ are given.
   The vector $\mathbf{r}=\mathbf{i}+2\mathbf{j}+\lambda\mathbf{k}$ is perpendicular to $\mathbf{p}$. Find the value of $\lambda$.2 marks
2. Relative to the origin $O$, the point $A$ has position vector $2\mathbf{i}+2\mathbf{j}+\mathbf{k}$ and the point $B$ has position vector $3\mathbf{i}-6\mathbf{j}+2\mathbf{k}$.
   Find the size of angle $AOB$, giving your answer in degrees to 1 decimal place.2 marks
3. The points $A$, $B$ and $C$ have coordinates $A(1,-1,2)$, $B(3,1,3)$ and $C(2,-3,0)$.
   Find the size of angle $BAC$, giving your answer in degrees to 1 decimal place.3 marks