Adding and subtracting vectors using vector diagrams

[Ishfa]

Homework Statement

Classical Mechanics

Relevant Equations

s= (a^2 + b^2 + 2ab cos alpha)^1/2

 

[BvU]

Look at the picture:
Doesn't it seem strange that

Check your math -- and is your calculator set up for radians or for degrees ?

$\$

 

[Steve4Physics]

Relevant Equations: s= (a^2 + b^2 + 2ab cos alpha)^1/2

View attachment 365813View attachment 365814

It would be best to sort out part a) first. There are some mistakes. The first two are:

1) The diagram is wrong. When adding vectors using a diagram, you draw the vectors 'tip-to-tail' or construct a suitable parallelogram.

2) The correct formula for the cosine law is $c^2 = a^2 + b^2~–~ 2ab \cos\alpha$ (where $\alpha$ is the internal angle between sides a and b). But you have used a plus sign.

Surprisingly I agree with $|\vec a + \vec b| = 4.4587$. It looks like some mistakes cancelled!

Minor edit.

 

[kuruman]

Surprisingly I agree with $|\vec a + \vec b| = 4.4587$. It looks like some mistakes cancelled!

The expressions for the magnitudes are obtained from
$|\mathbf a + \mathbf b|^2=(\mathbf a + \mathbf b)\cdot(\mathbf a + \mathbf b)=a^2+b^2+2ab\cos\alpha$
$|\mathbf a - \mathbf b|^2=(\mathbf a - \mathbf b)\cdot(\mathbf a - \mathbf b)=a^2+b^2-2ab\cos\alpha$
where $\alpha$ is the angle between the two vectors when placed tail-to-tail, here 125°.

In the vector diagram, $\vec S$ is the difference, but the calculation below it is correct for the sum.

 

[Steve4Physics]

In the vector diagram, $\vec S$ is the difference, but the calculation below it is correct for the sum.

The OP has incorrectly drawn the Post #1 diagram, believing (wrongly) that $\vec s = \vec a + \vec b$.

Then they have ignored their diagram and used:

Relevant Equations: s= (a^2 + b^2 + 2ab cos alpha)^1/2

which gives the correct value.

The OP should note thast the question specifically says “By constructing vector diagrams, find the magnitudes and directions of …”.

If the OP had used their (incorrect) diagram correctly, they would have obtained $|\vec S| \approx 8.4$.

 

[kuruman]

The OP has incorrectly drawn the Post #1 diagram, believing (wrongly) that $\vec s = \vec a + \vec b$.

Then they have ignored their diagram and used:

which gives the correct value.

The OP should note thast the question specifically says “By constructing vector diagrams, find the magnitudes and directions of …”.

If the OP had used their (incorrect) diagram correctly, they would have obtained $|\vec S| \approx 8.4$.

That's another way of looking at it.