56
Vectors
Q3.10
Any vector that points along a line at 45° to the
x
and
y
axes has components equal in magnitude.
Q3.11
A
B
x
x
=
and
A
B
y
y
=
.
Q3.12
Addition of a vector to a scalar is not defined. Think of apples and oranges.
Q3.13
One difficulty arises in determining the individual components. The relationships between a vector
and its components such as
A
A
x
=
cos
θ
,
are based on right-triangle trigonometry. Another problem
would be in determining the magnitude or the direction of a vector from its components. Again,
A
A
A
x
y
=
+
2
2
only holds true if the two component vectors,
A
x
and
A
y
, are perpendicular.
Q3.14
If the direction of a vector is specified by giving the angle of the vector measured clockwise from the
positive
y
-axis, then the
x
-component of the vector is equal to the sine of the angle multiplied by the
magnitude of the vector.
SOLUTIONS TO PROBLEMS
Section 3.1
Coordinate Systems
P3.1
x
r
=
=
°=

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