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Vocabulary
Complete the chart.
Word  Definition 
Unit Vector  __________________________________________________________________ 
___________  describes each of the x, y, and z components of the relevant vector 
___________  describe a vector as the result of individual magnitudes and directions as measured from the axes, starting at the origin 
Skew Lines  __________________________________________________________________ 
Vector Equation  __________________________________________________________________ 
___________  from a scientific standpoint is force multiplied by distance 
Vector Direction
What is the equation for a vector? _________________
For the figure above:
Write the equation of the angle between
What are the equations for the direction angles β and γ? _______________________ ______________________
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In your own words, describe the Pythagorean Property of Direction Cosines. __________________________________________________________________________
Hint: It establishes the equation
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What is the vector direction in degrees of the following 2dimensional vectors, assuming the positive xaxis is 0^{o} ?
 What is the direction of
⟨9,20⟩  What is the direction of
⟨2,18⟩  What is the direction of
⟨7,5⟩
Identify the directional cosines associated with the given vector:

P⃗=⟨75,30,102⟩  cos α =
 cos β =
 cos γ =

P⃗=⟨145,130,25.75⟩  cos α =
 cos β =
 cos γ =

P⃗=⟨220,300,175⟩  cos α =
 cos β =
 cos γ =
.
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Vector Equation of a Line
What is the standard form of a line? ______________________
We can specify a particular line in space by requiring that the equations for the two intersecting planes be _____________________. In a previous section we developed one equation for a plane given by d =  n_{x}x_{o } n_{y}y_{o } n_{z}z_{o }. In this case Qy + Px  QP = 0 and z = 0 must __________________ for all points on the line passing through points P and Q.
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If we already know the position vectors for two points on the line,
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In general, a vector equation is any function that takes any one or more ____________ and returns a ____________.
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Write the vector equation of the line defined by the the following points:

(−1,−1,7) and(3,11,8) 
(1,−3,2) and(−5,3,−1) 
(25,17,42) and(−16,12,23)

D⃗=⟨3,4,7⟩+d⟨3,3,2⟩ andF⃗=⟨−2,11,7⟩+f⟨−2,11,7⟩ 
D⃗=⟨15,3,−3⟩+d⟨3,11,8⟩ andF⃗=⟨5,3,6⟩+f⟨1,−4,6⟩
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Vector Analysis Applications
Vectors can be used in many reallife situations.
Work
The work done by forces can be determined using the ________________ of the force and the displacement vector
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Magnetic Force
The magnetic force can be described using the __________________ of the ______________ vector and the ______________ vector:
What is the metric baseunit of force? _______________
.
Torque
What is torque? __________________________________________________________
How do you find and describe the torque with vectors? __________________________________________________________
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 An fighter jet has a true airspeed of 1000 km/h due east. There is a cross wind blowing 60 degrees east of south at 100 km/h. Calculate the velocity of the jet relative to the ground.
 A bird is headed 40° east of north at 67 mph. A tail wind is blowing 45° west of south at 68 mph. Determine the direction of the bird.
 A fighter pilot with a mass of MA = 80 kg sits in the cockpit with his back horizontal to the ground. His jet is moving vertically with acceleration a. If the acceleration due to gravity on the pilot is g = 9.8 ms2, write a mathematical expression for and calculate the value of the reaction force R between the pilot and the back of his seat in the jet when:
 a = 0
 a = 8 ms2 upwards
 a = 8 ms2 downwards.
 Several evil villians are holding Spiderman in place with ropes. If FlatNose Frankie is pulling at a constant force of 19 pounds, 44° to the horizontal, GreenToe Gary is pulling at a constant force of 29 pounds along 31° to the horizontal, and JellyKnee Jennifyr is pulling at a constant force of 26 pounds at an angle of 33°, How hard and in what direction is OrangeChin Oswald pulling if Spiderman is stuck in place?