Maths problem with vectors

[Macko939]

Hi guys

I am studying for a maths test and I cant figure out one example...

 

So we need to calculate the angle between two vectors, S and T

 

I did few examples and I got the answers right except one of them and I just CANT figure out what am I doing wrong with this example

 

could you please point it out for me?

 

 

 

So the dot product is:

 

9 * (-2) + 12 * 6 + 18 * 7 = 180

 

And then:

|T| = sqrt(9² + 12² + 18²)

|T| = sqrt(549)

|T| = 23.43

so far so good. 

 

|S| = sqrt(-2² + 6² + 7²)

|S| = sqrt(81)

|S| = 9

 

|S| * |T| = 23.43 * 9 = 210.87

so we end up with 

θ = cos^-1(180 / 210.87)

When I tap that into the calculator it gives the answer 31.39°. 

The answer in the answer sheet is 35.48° and it is also the same when I tap in this question into WolframAlpha.

Something is clearly wrong with my workings but it seems like it's only happening when negative numbers are involved, since I can do other examples just fine and I get the right answer...

Please help!!!

[Bananasplit_00]

http://www.wolframalpha.com/

there you go, go there

[Macko939]

http://www.wolframalpha.com/

there you go, go there

 

Would be awesome if you'd at least read the entire post 

[Bananasplit_00]

Would be awesome if you'd at least read the entire post 

i did my best to help, im not that good with this stuff and Wolfram Alpha usiually has the answers, missed the part about that you had put it there but i think it probably comes down to how many decimals were used if it was shortened otherwise i have no idea

[Macko939]

-2^2 + 6^2 + 7^2 is not 81. It's 89.

 

Anything squared is positive. So -2^2 is 4, not -4

 

acos (180/(sqrt(89) x23.43)) is your answer

I just checked and for some reason my calculator says that -2² = -4. 

What the hell 

 

Thank you very much for pointing this out, I don't know how did I miss that...

 

i did my best to help, im not that good with this stuff and Wolfram Alpha usiually has the answers, missed the part about that you had put it there but i think it probably comes down to how many decimals were used if it was shortened otherwise i have no idea

 

I think I got the answer already, it was the calculator playing tricks on me...

[Macko939]

You have to put -2 in parenthesis.

 

(-2)^2 is 4, but the calculator sees -2^2 as (-1) x 2^2 = -4. It's a rule of thumb in calculus and pre-calculus that anything squared is positive.

 

I just blindly believed my calculator like a sheep and didn't even notice that squaring a negative gave a negative number, lol

[vanished]

 

I just checked and for some reason my calculator says that -2² = -4. 

What the hell 

 

Thank you very much for pointing this out, I don't know how did I miss that...

 

 

I think I got the answer already, it was the calculator playing tricks on me...

 

 

It could be how you typed it in. (see above)

[ionbasa]

When you're finding the magnitude of the vectors, leave them in exact form. Now plug this into to your calculator.

 

EDIT: Someone already caught your mistake. Use parentheses, always.

[DXMember]

I just blindly believed my calculator like a sheep and didn't even notice that squaring a negative gave a negative number, lol

baaaaaaaaaaaaaaa

[Macko939]

-2^2 + 6^2 + 7^2 is not 81. It's 89.

 

Anything squared is positive. So -2^2 is 4, not -4

 

acos (180/(sqrt(89) x23.43)) is your answer = 35.47779 ~ 35.48 degrees

 

 

It could be how you typed it in. (see above)

 

 

When you're finding the magnitude of the vectors, leave them in exact form. Now plug this into to your calculator.

 

EDIT: Someone already caught your mistake. Use parentheses, always.

 

 

baaaaaaaaaaaaaaa

 

Hey guys I just wanted to say that I managed to pass the test today. Thank you all for help !

[DXMember]

Hey guys I just wanted to say that I managed to pass the test today. Thank you all for help !

did you get any grade, or did you just 'pass'

[Nup]

I did vectors last semester, but it looked quite different, for two unknowns we solved it with a simultaneous equation. So maybe look that up.

EDIT; never mind, you seem to be doing it a different way :3

[Macko939]

did you get any grade, or did you just 'pass'

 

I got 60% which is Okay but not great, not too horrible either though. 

 

The pass threshold is 40%

[DXMember]

I got 60% which is Okay but not great, not too horrible either though. 

 

The pass threshold is 40%

wow.. that is terrible

my condolences

[Macko939]

wow.. that is terrible

my condolences

 

I'm just glad I passed so I don't have to resit it.

 

I didn't know that we had a test coming and I studied literally on the very last day for it and I was panicking that I'll fail it.

 

I got 92% for my first test though so my average is still decent-ish fr this module

 

My average right now is 76% so I'm still getting the best grade for this module (75%+) if I keep it until the end of the term

[Starelementpoke]

I'm just glad I passed so I don't have to resit it.

 

I didn't know that we had a test coming and I studied literally on the very last day for it and I was panicking that I'll fail it.

 

I got 92% for my first test though so my average is still decent-ish fr this module

My dad would kill me if I got that grade...

[Macko939]

My dad would kill me if I got that grade...

 

Well if you're old enough to go to university your parents shouldn't be involved anymore but that's just my opinion

[Starelementpoke]

Well if you're old enough to go to university your parents shouldn't be involved anymore but that's just my opinion

Nah, he´d still find me and kill me if he found out.

[Mathematical]

Well if you're old enough to go to university your parents shouldn't be involved anymore but that's just my opinion

 

If they are paying for the tuition and/or living expenses they should be.

[Mathematical]

My dad would kill me if I got that grade...

When I wrote tests for undergraduate classes, I tried to write the so the raw average would be a 70%-75%.