Subtracting/multiply vector clarification on worked problem

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In summary, the conversation covers a physics problem involving vector addition and subtraction. The two problems involve finding the magnitude and direction of vector C, which is equal to the sum and difference of vectors A and B. The first problem is solved using the Pythagorean theorem and trigonometry, while the second problem involves multiplying the components of vector B by a constant before adding them to the components of vector A. The correct vector for 4B must be used in the second problem.
  • #1
rfig08d
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Hello! I've been studying for physics and come across a problem that I've been working on from the textbook. I would just like some clarification as we have not fully covered this subject yet in the class sessions.

Homework Statement


A vector, Avector, has a magnitude of 15 w/ an angle of 25deg with x-axis, vector B has a length of 25 and makes an angle of 70 deg with x-axis. Compute the magnitudes and directions of the vectors: Cvector = Avector + 4*Bvector and Cvector = Avector - Bvector


Homework Equations


Problem 1: Cx = Ax - Bx and Cy = Ay - By

Problem 2: Bx = KAx and By = KAy


The Attempt at a Solution



For the 1st problem:

Ax = 13.6
Bx= 8.6
Ay = 6.3
By = 23.5
Leads to Cx = 5, Cy = -17.2
Size of Cvector = 17.9 from Pythagorean theorem
Angle of cvector = arctan (Cy/Cx) = -73.8

For the 2nd problem:

Bx = KAx = 4(13.6)= 54.4
By = KAy = 4(6.3) = 25.2

Now question here, since I have the multiplied 4B components, do I just treat the rest of the problem as an addition equation? So:

Cx = Ax + Bx and Cy = Ay + By

Cx = 13.6 + 54.4 = 68
Cy = 6.3 + 25.2 = 31.5


thank you for any help :)
 
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  • #2
rfig08d said:
Ax = 13.6
Bx= 8.6
Ay = 6.3
By = 23.5
Leads to Cx = 5, Cy = -17.2
Size of Cvector = 17.9 from Pythagorean theorem
Angle of cvector = arctan (Cy/Cx) = -73.8
Looks OK.
For the 2nd problem:

Bx = KAx = 4(13.6)= 54.4
By = KAy = 4(6.3) = 25.2
Why are you using the components of A? If B = (8.6, 23.5), then KB = (K*8.6, K*23.5).

Now question here, since I have the multiplied 4B components, do I just treat the rest of the problem as an addition equation?
Yes you do, but you need to find the correct vector for 4B.
 
  • #3
Oh wow, can't believe I didn't notice that beforehand.

I overlooked it because I was reading the textbook and saw the formula for multiple vectors of Bx = KAx.

Thanks for the help, greatly appreciate it!:)
 

FAQ: Subtracting/multiply vector clarification on worked problem

What is vector subtraction?

Vector subtraction is the process of finding the difference between two vectors. It involves subtracting the corresponding components of the two vectors to obtain a new vector.

How is vector subtraction performed?

To perform vector subtraction, you must first make sure that both vectors have the same number of dimensions. Then, you simply subtract the corresponding components of the two vectors to obtain the components of the new vector.

What is vector multiplication?

Vector multiplication is the process of multiplying a vector by a scalar (a single number). This results in a new vector with each component multiplied by the scalar.

How is vector multiplication performed?

To multiply a vector by a scalar, you simply multiply each component of the vector by the scalar value. The result will be a new vector with each component multiplied by the scalar.

How do I clarify a worked problem involving vector subtraction or multiplication?

To clarify a worked problem involving vector subtraction or multiplication, make sure you understand the steps and equations used in the solution. If you are still unsure, try plugging in your own values and working through the problem to see if you get the same result. You can also ask for help from a teacher or tutor.

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