Components along the same axis, say the
x -axis, are vectors along the same line and, thus, can be added to one another like ordinary numbers. The same is true for components along the
y -axis. (For example, a 9-block eastward walk could be taken in two legs, the first 3 blocks east and the second 6 blocks east, for a total of 9, because they are along the same direction.) So resolving vectors into components along common axes makes it easier to add them. Now that the components of
are known, its magnitude and direction can be found.
Step 3.To get the magnitude
of the resultant, use the Pythagorean theorem:
Step 4.To get the direction of the resultant:
The following example illustrates this technique for adding vectors using perpendicular components.
Adding vectors using analytical methods
Add the vector
to the vector
shown in
[link] , using perpendicular components along the
x - and
y -axes. The
x - and
y -axes are along the east–west and north–south directions, respectively. Vector
represents the first leg of a walk in which a person walks
in a direction
north of east. Vector
represents the second leg, a displacement of
in a direction
north of east.
Strategy
The components of
and
along the
x - and
y -axes represent walking due east and due north to get to the same ending point. Once found, they are combined to produce the resultant.
Solution
Following the method outlined above, we first find the components of
and
along the
x - and
y -axes. Note that
,
,
, and
.
We find the
x -components by using
, which gives
and
Similarly, the
y -components are found using
:
and
The
x - and
y -components of the resultant are thus
and
Now we can find the magnitude of the resultant by using the Pythagorean theorem:
so that
Finally, we find the direction of the resultant:
Thus,
Discussion
This example illustrates the addition of vectors using perpendicular components. Vector subtraction using perpendicular components is very similar—it is just the addition of a negative vector.
Subtraction of vectors is accomplished by the addition of a negative vector. That is,
. Thus,
the method for the subtraction of vectors using perpendicular components is identical to that for addition . The components of
are the negatives of the components of
. The
x - and
y -components of the resultant
are thus
Questions & Answers
Ayele, K., 2003. Introductory Economics, 3rd ed., Addis Ababa.
what's the difference between a firm and an industry
Abdul
firm is the unit which transform inputs to output where as industry contain combination of firms with similar production 😅😅
Abdulraufu
Suppose the demand function that a firm faces shifted from
Qd 120 3P
to
Qd 90 3P
and the supply function has shifted from
QS
20 2P
to
QS
10 2P .
a) Find the effect of this change on price and quantity.
b) Which of the changes in demand and supply is higher?
Demand curve shows that how supply and others conditions affect on demand of a particular thing and what percent demand increase whith increase of supply of goods
Israr
Hi Sir please how do u calculate Cross elastic demand and income elastic demand?
Abari
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