vectors - portland state university...express the vector f in terms of the unit vectors and . find...
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Vectors
Force Position Velocity
Vector quantity
In order to be completely spcified we need to know its MAGNITUDE and DIRECTION
Scalar quantity
AirplaneRabbit
v
g
X
Z
1D
1D
x v
v
y
X
Y
vector position
2D
Finding the vector components (with respect to a particular reference) Example
Example
Page 7
AzMagnitude of A = |A| � [ (Ax )2 + (Ay )2 + (Az )2 ]1/2
Unit Vector
That is,
Addition of Vectors By combining their axis components
Addition of Vectors Tail-to-tip graphic method
Example The same vector c expressed in different ways
Example
Page 16 EXAMPLE
j
i
u
45oF
F = 20 Kg-f
Unit of force
u = ?
Express the vector F in terms of the unit vectors and .
Find the unit vector whose direction is parallel to the ramp.
i j
=
Multiplication of Vectors
Scalar product
Geometrical interpretation of the scalar product
= +
+
-
The Vector Product
Z
X
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