How Can You Calculate the Magnitude of Vector A Using Dot Product Rules?

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Homework Help Overview

The discussion revolves around a physics problem involving the calculation of the magnitude of vector A using dot product rules. The problem includes vectors B and C, with specific angles and magnitudes provided, and seeks to establish a relationship between these vectors through their dot products.

Discussion Character

  • Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants explore the relationships between the angles and magnitudes of the vectors using trigonometric identities and equations derived from the dot product. There is an attempt to manipulate the equations involving cosine functions to find a solution.

Discussion Status

The discussion includes various attempts to derive equations from the given information, with one participant expressing confusion about the expansion of cosine functions and the subsequent steps. Another participant indicates they have resolved their issue, suggesting some progress in the discussion.

Contextual Notes

Participants are working under the constraints of the problem as stated, with specific angles and magnitudes provided. There is an indication of a potential misunderstanding in the manipulation of trigonometric identities, which remains unaddressed.

rambo5330
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Homework Statement


i'm having troubles solving this problem in physics involving dot product rule


Vector B is 5m and 60 degress above the x axis
A has the same magnitude as C and C is has 25 more degrees than A ..
find magnitude of A..
B dot C = 35
B dot A = 30

this all we're given.. as far as i can get it i make it down to two equations
cos(\theta + 25) = 7/C and cos(\theta) = 6/C
 
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The two equations should be

cos(θ-60 + 25) = 7/c...(1)
cos(θ-60) = 6/c ...(2)
divide (1) by (2), you get

\frac{cos(\theta-60 + 25))}{cos(\theta-60)} = 7/6

Let (θ - 60) = x
expand cos(x + 25) and divide it by cos(x)and simplify to find x.
 
excellent thank you,

I thought that was the method but I'm still running into trouble expanding cos(x + 25) and dividing to clear... when i expand i get


cosx / (cos(x))(cos(25)) - (sin(x))(sin(25)) = 6/7

i don't see how dividing that by cos(x) now accomplishes anything?

where am i going wrong?
 
nm its all good i got it figured out thanks !
 

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