The two vectors a with arrow and b with arrow in the figure below have equal magnitudes of 11.7 m and their angles are θ1 = 30° and θ2 = 106°.
(a) Find the x and y components of their vector sum r with arrow. (Express your answer in vector form.)
(b) Find the magnitude of r with arrow.
(c) Find the angle r with arrow makes with the positive x axis

- Ac3

- jamiebookeater

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- Ac3

a and b*

- Ac3

##### 1 Attachment

- anonymous

|dw:1442290286516:dw|

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## More answers

- anonymous

Vector form is i and j,
i represent x direction
j represent y direction.
like 5i+6j is 5 coordinates to the right and 6 to the north.
-5i-6j would be 5 coordinate to the left and 6 to the south.

- Ac3

what are the scalars for i and j of the resultant?

- Ac3

I know how to do this but keep getting the wrong answer for some reason.

- anonymous

|dw:1442290582101:dw|

- anonymous

Angle 1 and 3 are corresponding angles so they are the same.
Subtract 180 degrees from the (angles of 2 and 3) to get angle 5.

- anonymous

|dw:1442290969817:dw|

- anonymous

cos30=x/11.7
so 11.7cos30=x
You would get the x component for vector A
sin30=y/11.7
so 11.7sin30=y
You would get the y component for Vector B

- anonymous

Now try to get the x and y component for vector B.
After you get both, you would add the x component of vector A and B together to get the displacement or resultant x component.
Then do the same to get the resultant vectors y component.

- Ac3

That's the one I'm having trouble with Vector B

- Ac3

For vector A we can definitely do what you said, but not for vector B because it has a 106 degree angle.

- Ac3

Either that or my calculator is stupid.

- Ac3

ok so 164

- Ac3

ahhhh i see

- anonymous

Take that back.

- Ac3

I got -1.1 for the I of the resultant

- Ac3

Then what is it?

- anonymous

Nevermind, it works.

- Ac3

What do you get for the i and j values of the resultant?

- anonymous

How did you get 164 if you add 90 angles to angle 5?

- Ac3

angle 5 is 74

- Ac3

5,3 and 2 must add up to 180

- anonymous

Show me your math.

- anonymous

On how you get 74

- Ac3

Actually I can't even remember how I got to 74 now that I think of it.

- anonymous

180-30-106=?

- Ac3

oh yea 180=106

- Ac3

180-106

- anonymous

180=106?

- anonymous

Thats only 2.
You wrote angle 5,3,2 must add up to 180.

- Ac3

nvm on that.

- Ac3

5, and 2 must add up to 180

- anonymous

You were right on that.
And I said your 74 degrees on angle 5 is wrong.
Look at my drawings again.

- anonymous

|dw:1442292054233:dw|

- anonymous

|dw:1442292116154:dw|

- Ac3

then how do i find 5 and 2?

- anonymous

Look at your problem and information, not given by me.

- Ac3

That picture plus the words are the only information.

- anonymous

What is angle 3?

- Ac3

30

- Ac3

that doesn't help

- anonymous

and how do you know it is 30 degrees.
Wait up and you will see ok?

- Ac3

It's a geometry rule.

- anonymous

And how did you know angle 1 is 30 degrees?

- anonymous

Hint: information

- anonymous

So what is angle 2?

- anonymous

|dw:1442292824398:dw|

- Ac3

I have no idea

- Ac3

oh is that the 106?

- Ac3

Ok so I figured that out angle 5 is 44

- anonymous

But how did you know angle 1 is 30 degrees?
Please reread. -_-

- Ac3

It's a given

- anonymous

Yes it is 44

- anonymous

Whenever there is an angle that is not 0 or 90 or 180 degrees, I do not just assume the angle number.
It has to be given by the information.

- anonymous

I cant just guess that angle 1 is 30 degrees without info.

- Ac3

angle 1 is 30 that's a given.

- anonymous

Yes, so you should have no trouble knowing what angle 2 is.
Always read your question and information carefully.
It helps a lot in physics.

- anonymous

If I dont know what angle 2, I would not figure out how to do this.

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