two vectors x1 = (20 m) x and x2 (15 m) x, compute and show graphically (a) x1 + x2, (b) x1-x2 and (c) x2-x1
http://schools.wikia.com/wiki/Graphical_Vector_Addition
What is your subject?
"x1 = (20 m) x and x2 (15 m) x"
Does that mean they are both on the x axis?
To compute the addition and subtraction of vectors, you need to consider both their magnitudes and directions. Since the given vectors are in the same direction, the computation becomes simpler.
Let's start with vector addition:
(a) x1 + x2:
To add the vectors x1 and x2, you need to add their respective components. Since both vectors are in the x-direction, you can directly add their magnitudes:
x1 + x2 = (20 m) x + (15 m) x = (20 + 15) m x = (35 m) x
The resultant vector x1 + x2 has a magnitude of 35 meters and is in the x-direction.
Now, let's move on to vector subtraction:
(b) x1 - x2:
To subtract the vectors x2 from x1, you subtract their respective components:
x1 - x2 = (20 m) x - (15 m) x = (20 - 15) m x = (5 m) x
The resultant vector x1 - x2 has a magnitude of 5 meters and is in the x-direction.
(c) x2 - x1:
To subtract the vector x1 from x2, you subtract their respective components:
x2 - x1 = (15 m) x - (20 m) x = (15 - 20) m x = (-5 m) x
The resultant vector x2 - x1 has a magnitude of 5 meters and is in the opposite direction of the x-axis.
Now let's show these results graphically. Since all the vectors are in the x-direction, the graph will represent the x-axis.
Graphical representation:
(a) x1 + x2:
---->[35 m]
(b) x1 - x2:
---->[5 m]
(c) x2 - x1:
<----[-5 m]
In the graphical representation, the arrow indicates the direction of the vector, and the number beside it represents the magnitude in meters.