C4 Vectors Questions

Need help with question C!

7. The point A has position vector a = 2i + 2j + k and the point B has position vector
b = i + j – 4k, relative to an origin O.
(a) Find the position vector of the point C, with position vector c, given by
c = a + b.

(b) Show that OACB is a rectangle, and find its exact area.

The diagonals of the rectangle, AB and OC, meet at the point D.
(c) Write down the position vector of the point D.

(d) Find the size of the angle ADC.

I don't understand question C. If it is a rectangle then surely AB is the same as OC. so why can't D be 1/2AB and why is it 1/2OC

Not really sure what you are asking

The point D is the mid-pt of OC and it is also the mid-point of AB

The position vector OD is half OC but it is not half AB as that does not start at O

You could do OD = OA + half AB if you want to

Thanks!!! You answered my questions