Calculus 10.2 day 2

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10.2 day 2 Vector Valued Functions
Everglades National Park, FL
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Everglades National Park, FL
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Everglades National Park, FL
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Everglades National Park, FL
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Any vector can be written as a
linear combination of two standard unit vectors.
The vector v is a linear combination of the
vectors i and j.
The scalar a is the horizontal component of v and
the scalar b is the vertical component of v.
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We can describe the position of a moving particle
by a vector, r(t).
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In three dimensions the component form becomes
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Graph on the TI-89 using the parametric mode.
MODE
Graph.
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Graph on the TI-89 using the parametric mode.
MODE
Graph.
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Most of the rules for the calculus of vectors are
the same as we have used, except
Absolute value means distance from the origin
so we must use the Pythagorean theorem.
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Example 5
a) Find the velocity and acceleration vectors.
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Example 5
velocity
acceleration
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Example 5
speed
direction
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Example 6
slope
position
tangent
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Example 6
p