Radian Measurement

[Guest]

Help solving this problem.

Problem

Add the following vectors:


A = 3[b][e], θA = 1[c]4° and B = 2[c][d], θB = 3[a]8°

(Note: if PIN = 34659, then 3[b][e] = 349)

Round your answers to one decimal place.

[Guest]

Any comment about my problem?

[Guest]

It is quite difficult to understand your problem. If it was clear to me I would help you.

[Guest]

Your instructor should have assigned you a pin number. You have to have it to sold the problem.

[leesajohnson]

3[b][e] = 349

A= 3[b][e] as given

so 3[b][e] = 349 = A

A= 349

[Guest]

Sorry but I have no idea what "vector A= 3[b][e]" even means! Could you please explain the notation?

Nor do I understand how leesajohnson got "A= 349" when we wer told that A is vector not a number!

[Baltuilhe]

Help solving this problem.

Problem

Add the following vectors:


A = 3[ b][e], θA = 1[c]4° and B = 2[c][d], θB = 3[a]8°

(Note: if PIN = 34659, then 3[ b][e] = 349)

Round your answers to one decimal place.

Good afternoon!
PIN = 34659, then:
[a]=3
[ b]=4
[c]=6
[d]=5
[e]=9

So:
Data:
[tex]\begin{cases}\|\vec{A}\|=349&\theta_A=164^{\circ}\\\|\vec{B}\|=265&\theta_B=338^{\circ}\end{cases}[/tex]

Desired vector C:
[tex]\vec{C}=\vec{A}+\vec{B}[/tex]

Coordinates of vector A:
[tex]\|\vec{A_x}\|=340\times\cos\;164^{\circ}=-326,83\\
\|\vec{A_y}\|=340\times\sin\;164^{\circ}=93,72[/tex]

Coordinates of vector B:
[tex]\|\vec{B_x}\|=265\times\cos\;338^{\circ}=245,70\\
\|\vec{B_y}\|=265\times\sin\;338^{\circ}=-99,27[/tex]

Sum of vectors A and B:
[tex]\|\vec{C_x}\|=\|\vec{A_x}\|+\|\vec{B_x}\|=-81,13\\
\|\vec{C_y}\|=\|\vec{A_y}\|+\|\vec{B_x}\|=-5,55[/tex]

Now the solution:
[tex]\begin{cases}\|\vec{C}\|=\sqrt{81,13^2+5,55^2}=81,32\\
\theta_C=-\arctan\left(\dfrac{5,55}{81,13}\right)=-176,08^{\circ}\end{cases}[/tex]

I hope I have helped!

[dishatrivedi]

Great Solution.

[HallsofIvy]

How did you determine that "if PIN = 34659, then 3[ b][e] = 349"?

Is this some secret code that only the ELITE know?

[Guest]

It has dawned on me that "If PIN= 34659 then 3[b][e]= 349" because since in the alphabet, abcde, "b" is the second letter and "e" is the fifth letter, "[b]" is the second number, 4, and "[e]" is the fifth number, 9.

However, that "code" is NOT standard mathematics. If you want others to understand it, explainn it!

[GeradHum]

To add vectors A and B, you need to break each vector into its components and then add the corresponding components together. Vectors are typically represented in terms of their magnitude (length) and direction. The angle θ represents the direction, and the number in brackets represents the magnitude or length of the vector.

Let's break down vectors A and B:

Vector A:
Magnitude: 3
Direction: θA = 14°

Vector B:
Magnitude: 2
Direction: θB = 38°

Now, we'll find the components of these vectors in the x (horizontal) and y (vertical) directions:

For vector A:
Ax = 3 * cos(14°)
Ay = 3 * sin(14°)

For vector B:
Bx = 2 * cos(38°)
By = 2 * sin(38°)

Now, add the corresponding components together:

Resultant vector Rx:
Rx = Ax + Bx
Ry = Ay + By

Calculate Rx and Ry:

Rx = (3 * cos(14°)) + (2 * cos(38°))
Ry = (3 * sin(14°)) + (2 * sin(38°))

Calculate the values of Rx and Ry using a calculator:

Rx ≈ 2.9 (rounded to one decimal place)
Ry ≈ 2.0 (rounded to one decimal place)

So, the resultant vector R is approximately:

R ≈ 2.9[c] + 2.0[d]

Rounded to one decimal place, R is approximately:

R ≈ 2.9[c] + 2.0[d] (rounded)