Expert answers to "Vector A→ is 3.00 units in length and..."

lugreget9

Answered question

2021-12-14

Vector

\vec{A}

is 3.00 units in length and points along the positive x-axis. Vector

\vec{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

\vec{A} + \vec{B}

Answer & Explanation

GaceCoect5v

Beginner2021-12-15Added 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

\vec{A}

and

\vec{B}

. In the graph below, each square has a side of a length of 1 unite.

We notice that the length of the vector

(\vec{A} + \vec{B})

in the graph below is about 5 squares, meaning that its about 5 unites in length. The angle between

(\vec{A} + \vec{B})

and the positive x-axis can be calculated as follows:

θ = \tan^{- 1} (\frac{m i d B m i d}{m i d A m i d}) = \tan^{- 1} (\frac{4}{3}) = 53.13 °

However, notice that

(\vec{A} + \vec{B})

is in the fourth quarter, which means that

θ = - 53.13 °

m i d \vec{A} + \vec{B} m i d = 5

unites and makes an angle

θ = - 53.13 °

with the positive x-axis

Toni Scott

Beginner2021-12-16Added 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:

\vec{A} = (3, 0)

\vec{B} = (0, - 4)

We need to find

\vec{A} + \vec{B}

and

\vec{A} - \vec{B}

, their magnitude and direction.
For the magnitude we will use the formula to calculate the distance d between two points (pithagorean theorem):

d = \sqrt{{(Y 2 - Y 1)}^{2} + {(X 2 - X 1)}^{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:

\tan θ = \frac{Y 2 - Y 1}{X 2 - X 1}

(2)
Now, lets

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