# Thread: vector and dot product

1. ## vector and dot product

1. Work done is the product of the force and the distance travelled in the direction of the force. Calculate the work done when the force F=5i+3j moves an object from point P = ( -2 , 3 ) to point Q = ( 1 , 6 ).

2. Given thati = (1, 0) and j = (0,1), u= 2i +j, w= 3i+4j and v = i-3j
find,
a) u . v + u .w
b) (u.v)(u.w)

2. Originally Posted by dorwei92
1. Work done is the product of the force and the distance travelled in the direction of the force. Calculate the work done when the force F=5i+3j moves an object from point P = ( -2 , 3 ) to point Q = ( 1 , 6 ).

2. Given thati = (1, 0) and j = (0,1), u= 2i +j, w= 3i+4j and v = i-3j
find,
a) u . v + u .w
b) (u.v)(u.w)
1. W=F.s=(5i+3j).(3i+3j)=15+9=24

2. u.v=2-3=-1
u.w=6+4=10

a) u.v+u.w=-1+10=9

b) (u.v)(u.w)=-1.10=-10

3. could u write the working for qn 1?
i dont understand how u derived at 24...

4. Originally Posted by dorwei92
could u write the working for qn 1?
i dont understand how u derived at 24...
$F = 5i + 3j$

$\Delta r = (1,6) - (-2,3) = 3i + 3j$

$F \bullet \Delta r = (5 \cdot 3) + (3 \cdot 3) = 15 + 9 = 24$

5. why is it equivalent?

6. Originally Posted by dorwei92
why is it equivalent?
the basic definition of displacement ...

change in position = final position - initial position