When magnitude of addition is equals to

[H.D. M A K]

Mod note: Originally posted in a technical math forum, so missing the homework template.
How to find angle between two vectors when magnitude of both vectors and their resultant is given. for example The resultant of two vectors of magnitude 3n & 5n comes out 7N, the angle between vector is... please also explain how to solve it ...
Any help will be appreciated..
Thanks

 

[Quantum Defect]

How to find angle between two vectors when magnitude of both vectors and their resultant is given. for example The resultant of two vectors of magnitude 3n & 5n comes out 7N, the angle between vector is... please also explain how to solve it ...
Any help will be appreciated..
Thanks

You have three vectors with magnitudes a, b, & c
Align the coordinate system so that the x-axis lies along one vector. v_1 = (a,0). Let the other vector define the x-y plane. v_2 = (b*cos theta, b* sin theta)
The resultant vector v_3 is the sum of these two vectors (also lies in the x-y plane).

(1) v_3 = (a+b*cos theta, b* sin theta)

The square magnitude of v_1 is a^2, the square magnitude of v_2 is b^2, the square magnitude of v_3 is c^2

From (1) you can also write the square magnitude of v_3: a^2 + b^2 cos^2 theta + 2ab cos theta + b^2 sin^2theta = c^2

simplifying: a^2 + b^ 2 + 2ab cos theta = c^2

 

[berkeman]

<< 2 threads merged >>[/color]

 

[Mark44]

How to find angle between two vectors when magnitude of both vectors and their resultant is given. for example The resultant of two vectors of magnitude 3n & 5n comes out 7N, the angle between vector is... please also explain how to solve it ...

There is a much simpler way than what Quantum Defect proposed. You are given the magnitudes of two vectors, as well as their sum.

Write two equations that represent this information, and you'll have two equations in essentially two unknowns. It is not necessary to find the two vectors themselves.

An important equation is the following:
$$\cos(\theta) = \frac{\vec{u} \cdot \vec{v} } {|\vec{u}| |\vec{v}| }$$
where $\theta$ is the angle between the two vectors.

 

[H.D. M A K]

There is a much simpler way than what Quantum Defect proposed. You are given the magnitudes of two vectors, as well as their sum.

Write two equations that represent this information, and you'll have two equations in essentially two unknowns. It is not necessary to find the two vectors themselves.

An important equation is the following:
$$\cos(\theta) = \frac{\vec{u} \cdot \vec{v} } {|\vec{u}| |\vec{v}| }$$
where $\theta$ is the angle between the two vectors.

@Mark44 ,, still i am confusing to solve it till last step, would you like to solve it step by step. Values are given in the question...

 

[berkeman]

@Mark44 ,, still i am confusing to solve it till last step, would you like to solve it step by step. Values are given in the question...

It is your schoolwork question. You need to show us your work on trying to solve it first. That's part of the PF schoolwork help rules (see the "Info" link at the top of the page). :)

 

[H.D. M A K]

It is your schoolwork question. You need to show us your work on trying to solve it first. That's part of the PF schoolwork help rules (see the "Info" link at the top of the page). :)

@berkeman i am so bad in mathematics and even am stuck in simple calculations. Thanks for your sugesstion..

 

[Mark44]

please also explain how to solve it ...

@Mark44 ,, still i am confusing to solve it till last step, would you like to solve it step by step. Values are given in the question...

That's not how it works here -- we will help you, but we won't do the problem for you. What are the simple calculations you are stuck in? Show us what you have done, whether right or wrong, and we'll get you going in the right direction.