Transcript Unit Vector has the same direction as a given vector, but - abu-saba

6.6 Day 2
Objectives:
• Find the unit vector in the direction of v.
• Write a vector in terms of its magnitude & direction
• Solve applied problems involving vectors
Pg. 691 # 40-52 (even), 66-74 (even)
A Unit Vector has the same direction as a given
vector, but is 1 unit long
• Unit vector = (original vector)/length of vector
• Given vector, v = -2i + 7j, find the unit vector:
length  (2)  7  53
2
2
2
7
 2 53
7 53
unit :
i
j
i
j
53
53
53
53
1. Find the unit vector in the same direction as v = 4i – 3j.
Then, verify that the vector has magnitude (length) 1.
Writing a Vector in terms of
its Magnitude & Direction
• v is a nonzero vector. The vector makes an angle
measured from the positive x-axis to v, and we
can talk about the magnitude & direction angle of
this vector:
v  v cos  i  v sin  j
This is a vector in a form almost exactly
like polar form. The main distinction is
that the vector is not affixed to the
origin.
Velocity Vector: vector representing speed &
direction of object in motion
• Example: The wind is blowing 30 miles per hour
in the direction N20oE.
• Express its velocity as a vector v.
• If the wind is N20oE, it’s 70 degrees from the
positive x-axis, so the angle=70 degrees and the
magnitude is 30 mph.
v  30 cos(70)i  30 sin( 70) j
v  30(.34)i  30(.94) j  10.3i  28.2 j
2. The jet stream is blowing at 60 miles per hour in the direction S45oE.
Express its velocity as a vector v in terms of i and j.
Finding a Resultant Force
Use the provided formulas:
v  v cos  i  v sin  j
cos  
F  a 2  b2
a
F
3. Two forces F1 and F2, of magnitude 30 and 60 pounds, respectively, act on
an object. The direction of F1 is N10oE and the direction of F2 is N60oE. Find the
magnitude, to the nearest hundredth of a pound, and the direction angle, to the
nearest tenth of a degree, of the resultant force.