- #1
Help me find the vector and resultant magnitude of this equation pleas
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SUMMARY
This discussion focuses on the calculation of resultant vectors and their magnitudes using basic vector addition. The user presents two vectors, A = <1,2,3> and B = <2,1,3>, and seeks assistance in determining the resultant vector A + B and its magnitude |A + B|. Key concepts discussed include the use of trigonometric functions such as sine and cosine to find angles and relationships in right triangles, which are essential for solving vector problems in physics.
PREREQUISITES- Understanding of vector notation and representation (e.g., <1,2,3> or i + 2j + 3k)
- Basic knowledge of trigonometry, particularly Pythagorean theorem and sine/cosine functions
- Familiarity with vector addition and resultant vectors
- Ability to visualize vectors graphically on a coordinate plane
- Learn how to calculate the magnitude of a vector using the formula |A| = √(x² + y² + z²)
- Study vector addition techniques, including graphical methods and component-wise addition
- Explore trigonometric identities and their applications in solving vector problems
- Practice drawing and adding vectors using software tools like GeoGebra or Desmos
This discussion is beneficial for students in physics or mathematics, particularly those struggling with vector concepts, as well as educators seeking to clarify vector addition and magnitude calculations.
- #2
BiGyElLoWhAt
Gold Member
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How do you add vectors?
Vector A: <1,2,3> OR i + 2j + 3k
Vector B: <2,1,3> OR 2i + j + 3k
A + B = ?
|A| = ?
|B| = ?
|A + B| =?
Vector A: <1,2,3> OR i + 2j + 3k
Vector B: <2,1,3> OR 2i + j + 3k
A + B = ?
|A| = ?
|B| = ?
|A + B| =?
- #3
- #4
EverT23
- 3
- 0
I don't know How to add them, I have this physics online class that is little to No help on understanding this
- #5
BiGyElLoWhAt
Gold Member
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- 138
Ok, well let's try something here... I hope I don't get shunned for this lol.
How much do you actually know about vectors? Could you draw me some? View this picture, save it or hit print screen or however you want to get it, open it up in paint and grab yourself the straight line tool.
Can you draw, let's say, the vectors
<1,1>,
<1,2>,
&
<1,3>
?
Take each "tic" as 1 unit.
How much do you actually know about vectors? Could you draw me some? View this picture, save it or hit print screen or however you want to get it, open it up in paint and grab yourself the straight line tool.
Can you draw, let's say, the vectors
<1,1>,
<1,2>,
&
<1,3>
?
Take each "tic" as 1 unit.
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- #6
SteamKing
Staff Emeritus
Science Advisor
Homework Helper
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EverT23 said:
I take it you are completely innocent of trigonometry. You know, Pythagoras and all that.
- #7
- #8
SteamKing
Staff Emeritus
Science Advisor
Homework Helper
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EverT23 said:
The magnitude of the resultant looks OK. How about the angle the resultant makes with the horizontal?
- #9
BiGyElLoWhAt
Gold Member
- 1,637
- 138
As for the first, you have a couple right triangles that now share a common side, can you use that side (along with some trig) to make connections between the 2 triangles and ultimately get the side lengths you need?
As steam asked, trig and stuff.
Here's some useful equations (a quick google would give the same results)
##\text{sin}(\theta) = \frac{\text{side opposite of angle in a right triangle}}{\text{hypotenuse of aforementioned right triangle}}##
##\text{cos}(\theta) = \frac{\text{side adjacent to angle (not hypotenuse) in a right triangle}}{\text{hypotenuse of aforementioned right triangle}}##
You can multiply, divide, add, subtract, power, root, or whatever to both sides just like any equality to find a relationship for the particular side you're looking for. Just algebra those e q's and tell them what you want out of them.
As steam asked, trig and stuff.
Here's some useful equations (a quick google would give the same results)
##\text{sin}(\theta) = \frac{\text{side opposite of angle in a right triangle}}{\text{hypotenuse of aforementioned right triangle}}##
##\text{cos}(\theta) = \frac{\text{side adjacent to angle (not hypotenuse) in a right triangle}}{\text{hypotenuse of aforementioned right triangle}}##
You can multiply, divide, add, subtract, power, root, or whatever to both sides just like any equality to find a relationship for the particular side you're looking for. Just algebra those e q's and tell them what you want out of them.
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