11.2 Vectors
by SGLee - HSKim - JHLee
1-2. Determine 
.
1. (a) 
, 
(b) 
, 
(a) 
.
(b) 
.
Calculus-Sec-11-2-Solution
11.2 Vectors
by SGLee - HSKim - JHLee
1-2. Determine .
1. (a) ,
(b) ,
(a) .
(b) .
2. 
, 
AB=<-2-(-1),1-2,-2-3>=<-1,-1,-5>
3-4. Find the sum of the given vectors.
3. 
, 
.
5-8. Compute 
and 
.
5. 
, 
,
,
,
.
9. Determine a unit vector that has the same direction as 
.
The vector 
has length 
,
so the unit vector with the same direction is 
.
10. Find a vector that has the same direction as 
but has length 6.
http://matrix.skku.ac.kr/cal-lab/cal-11-2-10.html
11. A clothesline is tied between two poles, 6m apart. The line is quite taut and has negligible sag.
When a wet shirt with a mass of 0.8kg is hung at the middle of the line, the midpoint is pulled down 6cm.
Find the tension in each half of the clothesline.
Let 
and 
represent the tension vectors in each side of the clothe line as shown in the figure.
Then 
and 
have equal vertical components and opposite horizontal components,
so 
and 
. By similar triangles, 
.
The force due to gravity acting on the shirt has magnitude 
.
Hence we have 
. The resultant 
of the tensile forces counterbalances 
, so
and 
.
Thus, the tensions are 
.
12. The tension 
at each end of the chain has magnitude 50N.
What is the weight of the chain?
(b) Show, by means of a sketch, that there are scalars 
and 
such that 
.
(c) Find the exact values of 
and 
.
14. Let 
, 
, 
and 
in 
.
(i) Plot the vectors 
and 
.
(ii) Find scalars 
, 
and 
such that 
.
15. If 
and 
, describe the set of all points 
such that 
.
Therefore the surface of a sphere with a center 
and a radius 
.
4. 
, 
6. 
, 
8. 
13. (a) Draw the vectors 
, 
, and 
.