Vector \vec{A} is 3.00 units in length and points along

lugreget9 2021-12-14 Answered
Vector A is 3.00 units in length and points along the positive x-axis. Vector B is 4.00 units in tength and points along the negative y-axis. Use graphical methods to find the magnitude and direction of the vectors A+B
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Expert Answer

GaceCoect5v
Answered 2021-12-15 Author has 26 answers
Since we are asked to use a graphical method to solve the problem, we need to choose an appropriate scale to plot the vectors then measure the resulting vector from the addition of A and B. In the graph below, each square has a side of a length of 1 unite.

We notice that the length of the vector (A+B) in the graph below is about 5 squares, meaning that its about 5 unites in length. The angle between (A+B) and the positive x-axis can be calculated as follows:
θ=tan1(midBmidmidAmid)=tan1(43)=53.13°
However, notice that (A+B) is in the fourth quarter, which means that θ=53.13°.
midA+Bmid=5 unites and makes an angle θ=53.13° with the positive x-axis

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Toni Scott
Answered 2021-12-16 Author has 32 answers
Explanation:
Vectors in two dimensions have two components Y and X, and are written in the following form:
(X,Y)
In this case we have two vectors:
A=(3,0)
B=(0,4)
We need to find A+B and AB, their magnitude and direction.
For the magnitude we will use the formula to calculate the distance d between two points (pithagorean theorem):
d=(Y2Y1)2+(X2X1)2 (1)
For the direction, which is the measure of the angle the vector makes with a horizontal line, we will use the following formula:
tanθ=Y2Y1X2X1 (2)
Now, lets

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