First Year Mathematics A (Differentiation & Linear Algebra) (2 Viewers)

[Flop21]

Re: MATH1131 help thread

Calculating the area of the parallelogram with sides c,d, is |c X d|...

Why have they done that by root (7^3 + 7^3 + 7^3). I mean the ^3, instead of ^2???

 

[iforgotmyname]

Re: MATH1131 help thread

Calculating the area of the parallelogram with sides c,d, is |c X d|...

Why have they done that by root (7^3 + 7^3 + 7^3). I mean the ^3, instead of ^2???

What are you trying to say...

But area of parallelogram is cross product of c and d

 

[Flop21]

Re: MATH1131 help thread

One way (albeit not the best way) to find a vector perpendicular to a line is to just let your arbitrary vector x=(a,b,c)

Then x.u=0

But you can easily equate the components out and find any set of values for a, b and c that works.

Note: There is an arbitrarily large amount of vectors perpendicular to a line in R³. If you wanted to find a vector perpendicular to TWO lines this would be much harder, and the cross product would be employed.

Sorry I still don't understand how to do this. E.g:

L1 = <1,-,1> + t<0,2,3>

L2 = <1,4,6> + t<1,-3,2>

How do I use the dot product to show these two are perpendicular?

I've only used dot product with 2 single vectors only. Oh wait, or do I just use the directional vectors from both?

 

[iforgotmyname]

Re: MATH1131 help thread

Sorry I still don't understand how to do this. E.g:

L1 = <1,-,1> + t<0,2,3>

L2 = <1,4,6> + t<1,-3,2>

How do I use the dot product to show these two are perpendicular?

I've only used dot product with 2 single vectors only. Oh wait, or do I just use the directional vectors from both?

<0,2,3>.<1,-3,2>=0-6+6=0

 

[Flop21]

Re: MATH1131 help thread

What are you trying to say...

But area of parallelogram is cross product of c and d

Yes that "X" indicated cross product. But I was under the impression you need to find the | | of that to get the area.

 

[Flop21]

Re: MATH1131 help thread

<0,2,3>.<1,-3,2>=0-6+6=0

Okay cool, so that is a yes.

 

[leehuan]

Re: MATH1131 help thread

Okay cool, so that is a yes.

Yep just dot the direction vectors.

The area of the parallelogram is |a x b| (note IFMN forgot to put the abs value brackets around it)

But show me the original question.

 

[Red_of_Head]

Re: MATH1131 help thread

Sorry I still don't understand how to do this. E.g:

L1 = <1,-,1> + t<0,2,3>

L2 = <1,4,6> + t<1,-3,2>

How do I use the dot product to show these two are perpendicular?

I've only used dot product with 2 single vectors only. Oh wait, or do I just use the directional vectors from both?

You use the direction vectors, they're the ones that determine which way the vectors run.

1*0+2*-3+3*2=0

 

[Flop21]

Re: MATH1131 help thread

Yep just dot the direction vectors.

The area of the parallelogram is |a x b| (note IFMN forgot to put the abs value brackets around it)

But show me the original question.

What is | | again, I get so confused since they use it for so many things... absolute value... magnitude... length... whatever.



a, find the cross product c x d (answer is <7,7,-7>)

b, hence or otherwise find the area of the parallelogram with adjacent sides OC and OD, where O is the origin,

 

[Red_of_Head]

Re: MATH1131 help thread

| | is the magnitude. Generally every time | | comes up in algebra it will be magnitude.

 

[Flop21]

Re: MATH1131 help thread

| | is the magnitude.

which you find by root(a^2 + b^2 + c^2) right? Why they using ^3?

 

[leehuan]

Re: MATH1131 help thread

What is | | again, I get so confused since they use it for so many things... absolute value... magnitude... length... whatever.



a, find the cross product c x d (answer is <7,7,-7>)

b, hence or otherwise find the area of the parallelogram with adjacent sides OC and OD, where O is the origin,

All of them. It just depends on what context you're in what name you're SUPPOSED to give it. I always just say absolute value if I'm safe to.

If the answers wrote 7-cubed that is wrong

 

[Flop21]

Re: MATH1131 help thread

What's going on here, why does tan^-1 R turn into pi/2???

 

[leehuan]

Re: MATH1131 help thread

 

[Flop21]

Re: MATH1131 help thread

ohh

 

[Flop21]

Re: MATH1131 help thread

hitting the 12th hour of math study


including lunch tho

 

[Flop21]

Re: MATH1131 help thread

Use the mean value theorem to prove that for x>0


ln(1+x) > x/(1+x)

 

[Flop21]

Re: MATH1131 help thread

I still have no idea how to do those MAPLE matrix questions....

 

[iforgotmyname]

Re: MATH1131 help thread

Use the mean value theorem to prove that for x>0


ln(1+x) > x/(1+x)

That question is cancer period. Btw if you are doing past papers, i would recommend the 2015 one cause that one was a bit more harder than the rest

 

[integral95]

Re: MATH1131 help thread

I still have no idea how to do those MAPLE matrix questions....

I pretty much just rote learned that part lol, it's always the same type of computation.