http://www.ck12.org Chapter 7. Vectors
−→L+CON−−→+−−→CY N+−→T =< 0 , 0 >
< 8 ·cos 41◦, 8 ·sin 41◦>+< 10 ·cos 100◦, 10 ·sin 100◦>
+< 12 ·cos 200◦, 12 ·sin 200◦>+−→T =< 0 , 0 >Use a calculator to add all thexcomponents and bring them to the far side and theycomponents and then subtract
from the far side to get:
−→T ≈< 6. 98 ,− 10. 99 >Turning this component vector into an angle and magnitude yields how hard and in what direction he would have to
pull. Terry will have to pull with about 13 lb of force at an angle of 302. 4 ◦.
Vocabulary
Aunit vectoris a vector of magnitude one.
Component formmeans in the form<x,y>. To translate from magnituderand directionθ, use the relationship
<r·cosθ,r·sinθ>=<x,y>.
Thestandard unit vectorsare−→i which is the vector< 1 , 0 >and−→j which is the vector< 0 , 1 >.
Alinear combinationof vectors−→u and−→v means a multiple of one plus a multiple of the other.
Guided Practice
−→v =< 2 ,− 5 >,−→u =<− 3 , 2 >,−→t =<− 4 ,− 3 >,−→r =< 5 ,y>
B= ( 4 ,− 5 ),P= (− 3 , 8 )
- Solve foryin vector−→r to make−→r perpendicular to−→t.
- Find the unit vectors in the same direction as−→u and−→t.
- Find the point 10 units away fromBin the direction ofP.
Answers:
1.−→t has slope^34 which means that−→r must have slope−^43. A vector’s slope is found by putting theycomponent
over thexcomponent just like withriserun.
y
5 =−4
3
y=−^203- To find a unit vector, divide each vector by its magnitude.
−→u
|−→u|=<
√−^3
13 ,
√^2
13 >,
−→t
|−→t|=<