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|dw:1381109606282:dw| (Construct c = a + b)

|dw:1381109717758:dw|

I believe you are supposed to add them like this: |dw:1381110194843:dw|

I was trying to use the component method (x and y components)

What are the magnitudes of the two vectors?

Oh! I forgot to write that! One second...

|dw:1381111020150:dw|

|dw:1381111017373:dw|

255 or 75?

Oh!! Okay That makes sense!

No problem.

Hmmm I get 4.61 for magnitude?

7 degrees?

I got 4.62 magnitude, and -42.5 deg.

What did you get for Rx and Ry?

Rx: \(\ 5cos20+5cos255 \) \(\ = \) \(\ -0.13... \)
Rx: \(\ 5sin20 + 5sin255 \) \(\ = \) \(\ 0.416 \)

\(\ \huge \text{The latter should be } Ry. \)

Hmmm So perhaps the answer key is incorrect?

|dw:1381113129371:dw|

a - b = a + (-b)

|dw:1381114004562:dw|

Okay, and I would still add the components except add the OPPOSITE of the b components?

would x still be cos and y still be sin in this case? I always forget when those are switched

Where do the 135 and 240 come from?

It's subtraction, so shouldn't it be - 4.5cos240?

Let me explain that again.

|dw:1381114977171:dw|

These are the original vectors A and B, ok?

|dw:1381115051999:dw|

Instead of A + B, they want A - B, right?

Yup

Mathematically speaking, A + B is the same as A + (-B).
For example, 4 - 3 = 4 + (-3)

Yes

So in order to perform the subtraction of vectors A - B, we can instead add vectors A and -B.

Okay

The first step now is to find what the vector -B is.

If vector \(B = B_x + B_y\), then \(-B = -( B_x + B_y) = - B_x + (- B_y)\)

If B is the vector in the figure below,
|dw:1381115308130:dw|

uhuh

|dw:1381115353688:dw|

Those are the components of B.
Then this is -B:
|dw:1381115399994:dw|

ok

Since vector B goes up to the right, vector -B goes down to the left.

Now remember that we need to add vectors A and -B to subtract A - B.

|dw:1381115515926:dw|

There you have vector A and vector -B.
Now we need to add them.

First, let's translate the angles of the vectors to angles starting at the positive x axis.

|dw:1381115630429:dw|

okay

Now we get x and y components of both vectors.

ok

Ahhh! That makes more sense!

|dw:1381116568714:dw|