Vectors...help?

With respect to the origin O, the position vectors of points A, B and C are (2, 3), (4, -2) and (-3, -3) respectively.





(i) A point E (-2, p) is such that 2 |CE| = |AB|. Find the possible values of p.


Ans: - 5 1/2 or -1/2





(ii) Find the coordinates of the point Q if 2 CQ = BA + 1/2 AC.


Ans: (-5 1/4, -2)





Please help by showing workings...thanks

Vectors...help?
(i)





lABl = sqrt( (xB-xA)^2 + (yB-yA)^2) = sqrt(29)


lCEl = sqrt( (xE-xC)^2 + (yE-yC)^2) = sqrt( 10 + 6 p + p^2)





lABl = 2lCEl


=%26gt; AB^2 = 4 *CE^2


=%26gt; 29 = 4*( 10+6p + p^2)


=%26gt; 4p^2 +24p + 11=0


=%26gt; p= -1/2 or -11/2.





(ii)

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