vectors

[bumblebee123]

can anyone help me with this question?

question: PQRSTU is a regular hexaon PQ= a QR = b RS = c

a) express c in terms of a and b

any help would be really appreciated

 

[Harry_the_cat]

Mark the centre of the regular hexagon O.

PQ +QO = PO

Note that PQ = a, QO = c and PO = b, (using the properties of a reg hexagon)

So …..

 

[bumblebee123]

Mark the centre of the regular hexagon O.

PQ +QO = PO

Note that PQ = a, QO = c and PO = b, (using the properties of a reg hexagon)

So …..

QO (c) = PO - PQ

c = b - a

this is correct, thanks


part b) says:x is the midpoint of PU and Y is the midpoint of ST express XY in terms of a and b

i thought that PO = b and OS = b

so PS = 2b

but I don't know how I'm supposed to find XY

 

[Dr.Peterson]

XY = XU + UT + TY.

 

[bumblebee123]

XY = XU + UT + TY.

XY = 1/2 c + b + 1/2 a

 

[Dr.Peterson]

Now finish: what is it in terms of a and b?

 

[bumblebee123]

Now finish: what is it in terms of a and b?

haha, I don't know why I thought I couldn't finish it.

c = b - a

so

XY = 1/2 ( b- a ) + b + 1/2 a
XY = 1/2 b - 1/2a + b + 1/2 a
XY = 3/2 b

which is the correct answer!

thank you so much for all of your help!