# Vector worked examples

Example 1

Write in terms of a  and b  the vector vec (BC)

Think of this as two separate vectors

Therefore

vec (BC)=-a+b

Or vec (BC)=b-a

Example 2

vec (AB)=m

vec (AD)=n

The point C  on BD  is such that:

BC:CD=1:3

i.  Find D  to B  in terms of n  and m

Think of this as the separate vectors

Therefore

vec (DB)=-n+m

Or vec (DB)=m-n

vec (DB)=-n+m=m-n   (The latter is chosen because it's neater)

ii. Find vec (AC)  in terms of m  and n

remember

We are told BC:CD=1:3

this means

which also means

which also means

So if we redraw the original diagram

vec (AC)  in terms of m  and n  are:

vec (AC)=n+3/4m-3/4n

vec (AC)=3/4m+1/4n

OR

vec (AC)=m-(1/4m-1/4n)

vec (AC)=m+(-1times(1/4m-1/4n))

vec (AC)=m-1/4m+1/4n

vec (AC)=3/4m+1/4n

Both get the same answer (as they should)

vec (AC)  in terms of m  and n=3/4m+1/4n

Example 3

If AD  is parallel to CB  and AB  is parallel to DC, write in terms of a  and b  the vectors vec (BC)  and vec (BA)

vec (BC)=a
vec (BA)=-c