0606 P21 - Jun 2021 - Q10 - 8 marks
7981
Relative to an origin \(O\), the position vectors of the points \(A\), \(B\), \(C\) and \(D\) are
\(\overrightarrow{OA}=\binom{6}{-5},\quad \overrightarrow{OB}=\binom{10}{3},\quad \overrightarrow{OC}=\binom{x}{y},\quad \overrightarrow{OD}=\binom{12}{7}.\)
(a) Find the unit vector in the direction of \(\overrightarrow{AB}\).
(b) The point \(A\) is the mid-point of \(BC\). Find the value of \(x\) and of \(y\).
(c) The point \(E\) lies on \(OD\) such that \(OE:OD=1:1+\lambda\). Find the value of \(\lambda\) such that \(\overrightarrow{BE}\) is parallel to the \(x\)-axis.
