MCV4U1

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MCV4U1
5.5 - Applications of the Dot and Cross Product
Projections - The mapping of a geometric figure
formed by "dropping a perpendicular "
from each point on the figure onto a
line or plane.
Ex.)
Q
P
A
R
? PA is the projection of PQ onto PR
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Developing the Projection Formula
y
Let OA be the projection of u onto v.
u
v
?
A
x
But
O
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Developing the Projection Formula cont....
Since OA is a portion of v, we can write the
vector OA as
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Ex.) Find the specified projections if u (3,
-1, 2), v (2, 5, -2), w (1, 0, 3)
b)
a)
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Area of a Parallelogram
Area (Base)(Height)
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Ex.) Find the Area of the parallelogram formed
by the vertices A(1, 1, 2) B(-3, 5, 6) C(7,
-2, -5) D(-1, 3, 4)
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Volume of a Parallelepiped
Parallelepiped - A 3-dimensional parallelogram,
where opposite faces are parallel and
congruent parallelograms.
Volume (Area of Base) (Height)
1) Area of Base
2) Height
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? Volume
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Ex.) If a (1, 1, 3), b (2, 0, 4) and c (1,
2, 1) Find the volume of the parallelepiped
formed by these vectors.
Homework p.192 1, 3, 4, 6, 7, 8
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