# vector and dot product

• Oct 17th 2009, 02:27 AM
dorwei92
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)
• Oct 17th 2009, 04:10 AM
alexmahone
Quote:

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
• Oct 17th 2009, 05:02 AM
dorwei92
could u write the working for qn 1?
i dont understand how u derived at 24...
• Oct 17th 2009, 05:23 AM
skeeter
Quote:

Originally Posted by dorwei92
could u write the working for qn 1?
i dont understand how u derived at 24...

$\displaystyle F = 5i + 3j$

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

$\displaystyle F \bullet \Delta r = (5 \cdot 3) + (3 \cdot 3) = 15 + 9 = 24$
• Oct 17th 2009, 05:59 AM
dorwei92
• Oct 17th 2009, 06:24 AM
skeeter
Quote:

Originally Posted by dorwei92

the basic definition of displacement ...

change in position = final position - initial position