- #1
realism877
- 80
- 0
Homework Statement
Vector a =8
vector b=15
the solution is 9 and theta is 34 degrees
I want to know how did they come up with that solution.
In summary: Similarly, b points to the left, which is either 180 degrees or -180 degrees with respect to the +x direction.So, the angle of a is -90 degrees and the angle of b is -180 degrees. To find the angle of the sum, you can use trigonometry or the Pythagorean theorem. Using the Pythagorean theorem, we get:c^2 = a^2 + b^2c = √(8^2 + 15^2) = √289 = 17To find the angle, we can use trigonometry:tanθ = (opposite/adjacent) = (15/8)θ = tan^-1(15/
Vector a =8
vector b=15
the solution is 9 and theta is 34 degrees
I want to know how did they come up with that solution.
- #2
anonymity
- 163
- 0
You are either missing information, or neglecting to post it.
A vector has a magnitude and a direction. What you posted for a and b has the magnitude part down, but is missing direction.
Is this all you were given?
(this will likely be moved -- but I'm not an admin so oh well for now)
A vector has a magnitude and a direction. What you posted for a and b has the magnitude part down, but is missing direction.
Is this all you were given?
(this will likely be moved -- but I'm not an admin so oh well for now)
- #3
realism877
- 80
- 0
Here is the image of the solutionanonymity said:
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- #4
gb7nash
Homework Helper
- 805
- 1
realism877 said:
Are you sure you wrote this correctly? Is this magnitude? The actual vector? Euclidean vectors have a magnitude and a direction. I guess you could have vectors in R1, where there's only two directions (positive and negative).
However, the presence of an angle and an incorrect magnitude suggest to me that this is not the case. You need to elaborate.
- #5
realism877
- 80
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We have to find the magnitude and direction of the sum of vector A and B.
- #6
gb7nash
Homework Helper
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Ok, so how do you typically add vectors together?
- #7
realism877
- 80
- 0
Yes
And get the angle
And get the angle
- #8
realism877
- 80
- 0
Do I use the law of sines or just the pythogrean theorem?
- #9
realism877
- 80
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I know how to get 9 as the solution. HOwever, I don't know how they got 34 degrees as a solution.
- #10
- 12,180
- 182
You need to express each vector in terms of x and y (or horizontal and vertical) components. You should have either been shown this in your class, or it would be in your textbook as well.
As gb7nash asked, how have you been shown, in your class, to add vectors?
As gb7nash asked, how have you been shown, in your class, to add vectors?
- #11
realism877
- 80
- 0
I got how to add them, but how do I find the difference?
I need help finding the angles. How do I do that?
I know I have to put b in the negative direction. Which I did, but what is its angle? What is the angle of a?
I need help finding the angles. How do I do that?
I know I have to put b in the negative direction. Which I did, but what is its angle? What is the angle of a?
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- #12
- 12,180
- 182
tanθ = (y component of vector) divided by (x component of vector)realism877 said:
The angle of b will change by 180 degrees when you put it in the opposite direction.
From the figure you posted earlier, a points straight down. That would be either 270 degrees or -90 degrees with respect to the +x direction.
FAQ: How to Find Vector Angles and Differences?
1. What is the definition of vector addition?
Vector addition is the mathematical operation of combining two or more vectors to produce a resulting vector. It is represented by the "+" symbol and follows the commutative and associative properties.
2. How do you find the sum of two vectors using components?
To find the sum of two vectors using components, you add the corresponding components of each vector together. For example, if vector A is (3,1) and vector B is (2,5), then the sum of A and B would be (3+2, 1+5) = (5,6).
3. What is the difference between vector addition and scalar multiplication?
Vector addition involves combining two or more vectors to produce a resulting vector, whereas scalar multiplication involves scaling a vector by a scalar quantity (a number). Scalar multiplication only affects the magnitude of the vector and not its direction, whereas vector addition affects both magnitude and direction.
4. Can vectors with different dimensions be added together?
No, vectors with different dimensions cannot be added together. In order to add two vectors, they must have the same number of components and be in the same direction.
5. How is the sum of two vectors represented graphically?
The sum of two vectors is represented graphically by the vector resulting from placing the initial point of the second vector at the terminal point of the first vector. The resulting vector is the sum of the two vectors and is represented by an arrow with its initial point at the initial point of the first vector and its terminal point at the terminal point of the second vector.