Vectors question ?

OABC is a parallelogram.


---%26gt; ---%26gt;


OA = (1/2), OC = (4/0)


a) find the vector OB as a column vector?


b) X is the oint on OX such that OX=kOB, where 0%26lt;k%26lt;1


Find in terms of k, the vectors


i) OX ii) AX iii) XC


c) Find the value of k for which AX=XC





THANK YOU SO MUCH FOR ANY HELP

Vectors question ?
a)


OB is the sum of OA and OC, or (5,2). As a column vector, just write it as a 2x1 matrix with entries 5 and 2, reading down.





b)


OX = kOB is given.


AX = kOB - OA = OX - OA


XC = OC - kOB = OC - OX





c)


Set AX and XC as equal,


AX = OX - OA


XC = OC - OX


so,


OX - OA = OC - OX


2 OX = OA + OC


2 OX = OB = (5,2)


OX = 1/2 OB = (2.5,1)


k = 1/2