6.3 NOTES
COMPONENT FORM
MAGNITUDE
pp 18­22
Answer to p 457 #56
0 = 141.34o
18
The key to doing these is to find the unit vector first (unit vector's mag = 1)
Also, make sure to rationalize
unit vector
You want your vector to have a Magnitude=3
unit vector
You want your vector to have a Magnitude=2
18
unit vector
You want your vector to have a Magnitude=5
Linear combination Linear combination Find the component form of v given its magnitude
and the angle it makes with the positive x­axis:
19
NOTE: Since we are on the trig circle (radius=1), the vector is already a unit vector
length/magnitude
1. v =2 angle θ = 450
( ) point
< > vector
2. v = 25
θ = 1200
2< > = < >
,
Note: you are no longer on the trig circle for this problem. So, find the unit vector and multiply by 4
Find the component form of v where u = 3i ­ j and w = i + 4j :
3
1. v = u
2
3. v = u ­ 3w
2. v = u + 2w
1
4. v = (3u + w)
2
20
force of 600 pounds is required to pull a boat and trailer up a 22
1. Aramp
at 15 from the horizontal. Find the combined weight of
the boat and trailer.
Force of
Gravity
Answer
Force Against
the Ramp
Homework problem p 22
120
120
sin 120= llACll
llBAll
0 = llACll
llBAllsin 12
0 = 500
llBAllsin 12
sin 120 sin 12 0 llBAll = 2,404.87
AC = 500 Answer The combined weight of the boat and trailer is 2,404.87 lbs