1.4: Position vectors and a unit vector

4PM1/2R/June/2022 — Question 1 · 5 marks

The position vector of the point A\displaystyle A is 3i−2j\displaystyle 3\mathbf{i}-2\mathbf{j}, referred to a fixed origin O\displaystyle O.
The point B\displaystyle B is such that
AB→=6i+8j.\overrightarrow{AB}=6\mathbf{i}+8\mathbf{j}.
(a) Find the position vector of B\displaystyle B as a simplified expression in terms of i\displaystyle \mathbf{i} and j\displaystyle \mathbf{j}.
(2)
(b) Find the magnitude of AB→\displaystyle \overrightarrow{AB}.
(1)
(c) Find a unit vector, in terms of i\displaystyle \mathbf{i} and j\displaystyle \mathbf{j}, that is parallel to AB→\displaystyle \overrightarrow{AB}.
(2)