00:01
In this question we're given that oa b c is a parallelogram and oa, vector oa is given by a and vector oc is given by c.
00:10
So let's draw this, represent this information on a diagram so i'm just going to draw a parallelogram and i'll call it oa b c.
00:29
Then the vector oa is given as a and the vector oc is given as c and the vector oc is given as c.
00:38
The diagonals intersect at f.
00:41
So you need to join these points o and b and point c and a so that we get a diagonal at f.
00:52
The diagonals intersecting at f and e is a midpoint of fb.
00:59
So we have a point e which is a midpoint of.
01:04
So these two parts are congruent f e and e b.
01:09
So we're going to express the following terms.
01:15
We're going to express the following terms of a and c.
01:20
So this diagram is going to be useful in getting these expressions.
01:24
So the first expression we want is ef.
01:29
E, e, f, then the second one will be e.
01:35
Okay.
01:36
Now ef is part of b -o.
01:44
So what we want to do for us is to get an expression for b or even o b and and so this is how we're going to to get that we know that ac o c is parallel to ab so this vector ab is also given by c and the vector o a sorry or a vector oa is parallel to c b so this two will also be both represented by vector a.
02:29
Now let's determine the value of vector b -o, actually o or o b.
02:37
Let's start with o b.
02:39
Now the vector ob is going to be represented by vector oc plus c b and this is equal to c plus a.
02:59
Now we know know in a parallelogram that the diagonals bisect each other.
03:05
So the vector f, fb, is going to be half of vector ob.
03:16
So vector fe is half of, sorry, f is half of the half of v.
03:31
So this is going to be half of vector ob.
03:34
Will be...