# chapter6 4 by dOKeRm1

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```									Find ||u||.
1. u  1, 2
2. u  4i  3 j
The points A and B lie on the circle x  y  4.
2   2

Find the component form of the vector AB.
3. A  (1, 3), B  (2,0)
4. A  (1, 3), B  (2,0)
5. Find a vector u with the given magnitude in the
direction of v. ||u||  3, v  2, 4
Find ||u||.
1. u  1, 2     5
2. u  4i  3 j 5
The points A and B lie on the circle x  y  4.
2    2

Find the component form of the vector AB.
3. A  (1, 3), B  (2, 0)     1,  3

4. A  ( 1, 3), B  (2, 0)    3,  3
5. Find a vector u with the given magnitude in the
direction of v. ||u||  3, v  2, 4    1.34, 2.68
The dot product or inner product of u  u , u
1     2
and
v  v ,v
1   2
is u  v  u v  u v .
1   1   2   2
Find the dot product.
4,3  1, 2
Find the dot product.
4,3  1, 2

4,3  1, 2  (4)(1)  (3)(2)  10
If  is the angle between the nonzero vectors u and v , then
uv                     uv 
cos           and      cos 
-1

|u| v                    |u| v 
       
Find the angle between the vectors u  3, 2 and v  1,0 .
Find the angle between the vectors u  3, 2 and v  1,0 .

     uv   
  cos 1

     u v   
           
     3, 2  1,0 
  cos -1

     3, 2 1,0 
                
            
3
 cos -1


     
13 1 

 33.7
If u and v are nonzero vectors, the projection of u onto
 uv 
v is proj u        v.
 v 
v         2

     
If F is a constant force whose direction is the same as
the direction of AB, then the work W done by F in
moving an object from A to B is W || F |||| AB ||

```
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