Advanced Precalculus Notes 8.4 Vectors

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Advanced Precalculus Notes 8.4 Vectors

• Vector a quantity which has both magnitude
  (represented by length of arrow) and direction.
• If a vector represents the speed and direction of
  an object, it is a velocity vector. If it
  represents direction and amount of force acting
  on an object it is a force vector.
•  
• Directed line segment has initial
  point P1 and terminal point P2. The magnitude is
  the distance from point P1 to P2.
•  
• Zero vector no magnitude and no direction.
•  
• Unit vector A vector with length (magnitude)
  one, but the same direction as the original
  vector. The unit vector in the horizontal
  direction is i and in the vertical direction is
  j.

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Standard position of a vector initial point is
the origin (0, 0)   Component form of a vector v
initial point and terminal point vector v
  Magnitude of vector v   Equivalent
vectors have the same length (magnitude) and
direction.   Scalar product A vector in which
each component is multiplied by the scalar,
affecting magnitude but not direction.
3
Find the position vector of the vector if
and and graph both the
original vector and the position vector.
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Vector addition Read properties of vectors
page 609 commutative, associative, additive
identity, additive inverse properties.
5
Let v lt3, 3gt and u lt-3, 1gt find
each specified vector, write it in component
form, graph it and find its magnitude.   a) u
v b) 2u v c) v ½ u
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Find a unit vector in the direction of v 4i
3j
A ball is thrown at an initial speed of 25 miles
per hour in a direction that makes an angle of
30º with the positive x-axis. Express the
velocity vector v in terms of i and j. What is
the initial speed in the horizontal direction?
What is the initial speed in the vertical
direction?
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Static Equilibrium object is at rest and the sum
of all forces acting on the object is ZERO.   A
box of supplies that weighs 1200 pounds is
suspended by two cables attached to the ceiling,
as shown. What is the tension in the two
cables?  
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Assignment page 618 1 9, 16 22 even, 23,
27, 33, 39, 49, 51, 53, 61, 66