Vectors in three dimensionsAQA A-Level Maths: Mind map

Exam questions on Vectors in three dimensions

1. The vectors $\mathbf a=2\mathbf i-3\mathbf j+6\mathbf k$ and $\mathbf b=\mathbf i+2\mathbf j-2\mathbf k$.
   Find the exact distance between the points with position vectors $\mathbf a$ and $\mathbf b$.2 marks
2. The points $A$ and $B$ have position vectors $\mathbf a=\mathbf i+2\mathbf j+3\mathbf k$ and $\mathbf b=4\mathbf i-2\mathbf j+15\mathbf k$ relative to the origin $O$.
   The point $C$ is such that $\overrightarrow{AC}=2\overrightarrow{AB}$. Find the position vector of $C$.2 marks
3. $\mathbf u=2\mathbf i-\mathbf j+4\mathbf k$, $\mathbf v=-6\mathbf i+3\mathbf j+\mu\mathbf k$ and $\mathbf w=2\mathbf i+3\mathbf j+q\mathbf k$, where $\mu$ and $q$ are constants.
   Given that $\mathbf u$ and $\mathbf v$ are parallel, find the value of $\mu$.3 marks