Magnitude, direction and position vectorsAQA A-Level Maths: Mind map

Exam questions on Magnitude, direction and position vectors

1. The vector $\mathbf p=5\mathbf i-12\mathbf j$.
   Find a unit vector in the direction of $\mathbf p$.2 marks
2. The points $A$ and $B$ have position vectors $\mathbf a=2\mathbf i+3\mathbf j$ and $\mathbf b=8\mathbf i-5\mathbf j$ relative to the origin $O$.
   The point $C$ has position vector $3\mathbf a$. Find the exact distance $AC$.2 marks
3. The vector $\mathbf v$ has magnitude $8$ and direction $150^\circ$, measured anticlockwise from the positive $x$-direction. The vector $\mathbf w=4\sqrt3\,\mathbf i+3\mathbf j$.
   Express $\mathbf v$ in the form $x\mathbf i+y\mathbf j$, giving exact values of $x$ and $y$.3 marks