Question

The diagram shows a trapezium ABCD in which BA is parallel to CD.
(ii) Given that the length of CD is 12 units, find the position vector of D.

Diagram : http://onlineexamhelp.com/wp-content/uploads/2014/08/9709_s14_qp_12.pdf

Answer 1

I'm not sure if this helps but does ACD triangle being a right triangle give you any hints to a possible solution?

Answer 2

no.

Answer 3

BA and CD is parallel. So, yeah.

Answer 4

AB is -2i-j+2k

Answer 5

AB is a ration of CD. Using that and the process you used to determine AB and apply it to CD can't you find the position vector of D?

Answer 6

Definitely, no. Or else I won't have posted here. lol.

Answer 7

Can you tell us what you have done so far in solving the problem?

Answer 8

I couldn't figure out anything.

Answer 9

Oh sorry I've found things like the scalar value of the position vector D and some other things. I can also find the k value of position vector D but thats pretty much it.

Answer 10

Didnt learn this yet o.o

Answer 11

@phi @.Sam. @iambatman

Answer 12

AB means the vector B-A
(OA means A - O but O is zeros, so that simplifies to A)
similarly BC is C-B

so find AB and BD and perform the dot product. You should get 0.

Answer 13

for part ii)
D (or, the same thing, OD) is OC + 12 v
where v is the *unit length* vector in the direction you want to go.
the direction you want to go is BA = A-B
make it a unit vector by dividing by its magnitude. in other words v= (A-B)/|A-B|

Answer 14

How do I work it out?

Answer 15

which part?

Answer 16

CD = CO + OD
CD + OC = OD
12v + (4i + 5j +6k) = O Then?

Answer 17

OD *

Answer 18

we really don't want CD per se
(which we can't find until we know D, which is what we are trying to find.)

Answer 19

we use this idea:
we add the vectors OC and 12 v
where v is in the *same direction* as CD
we know how to find a vector in the same direction: AB is in the same direction.

Answer 20

Ah. got it! thankss.