3.31: Displacement, distance and section formula

0606/11/O/N/23 — Question 3 · 5 marks

Point AA has position vector (2−6)\begin{pmatrix} 2 \\ -6 \end{pmatrix} and point BB has position vector (−36)\begin{pmatrix} -3 \\ 6 \end{pmatrix}.
(a)
Find, in vector form, the displacement of BB from AA.
[2]
(b)
Find the distance ABAB.
[1]
(c)
Point XX is such that 3AB→=2AX→3\overrightarrow{AB} = 2\overrightarrow{AX}. Find the position vector of XX.
[2]