Dot product vector question

[rambo5330]

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

 

[rl.bhat]

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.

 

[rambo5330]

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?

 

[rambo5330]

nm its all good i got it figured out thanks !

 

[rwisz]

Hello,

Thank you for reaching out with your question. It seems like you are working on a problem involving the dot product rule in physics. The dot product is a mathematical operation that takes two vectors and returns a scalar value. It is used to determine the angle between two vectors and to calculate work and energy in physics.

In your problem, you are given the magnitude and direction of vector B, and you need to find the magnitude of vector A. The dot product of B and C is given to be 35, and the dot product of B and A is 30. From this information, we can set up the following equations:

B dot C = |B||C|cos(theta) = 35
B dot A = |B||A|cos(phi) = 30

Where theta is the angle between B and C, and phi is the angle between B and A. We can also use the fact that A and C have the same magnitude to set up another equation:

|A| = |C|

From here, we can use trigonometric identities to solve for |A|. By substituting |C| for |A| in the second equation, we get:

|B||C|cos(phi) = 30
|B||A|cos(phi) = 30
|B||C|cos(phi) = 30

Since |B| and |C| are known values, we can solve for cos(phi). Then, using the inverse cosine function, we can solve for phi, which is the angle between B and A. Finally, we can use the dot product equation to solve for |A|:

|A| = 30 / (|B|cos(phi))

I hope this helps you solve your problem. Remember to always use the appropriate equations and trigonometric identities when working with dot products. If you continue to have trouble, I suggest reaching out to your teacher or a classmate for further assistance. Good luck with your studies!

Best,