Math Is Fun Forum

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Vector 2

Question 2
Find a vector perpendicular to each of the vectors
A vector =2i+j+k
b vector =4i+2j-k

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Malik

Bob

Administrator

Registered: 2010-06-20

Posts: 10,140

Re: Vector 2

hi Zeeshan 01

If you call the vector ai + bj +ck and use the dot (scalar) product you'll get two equations in a, b and c.

Eliminate c and choose an arbitrary value for, say, 'a' so you can express b and c in terms of this.  It's ok to choose 'a', as any vector parallel to the one you calculate would also satisfy the requirements.

I think I can also do your other vector question, but I need time to remind myself how this is done.  I'll try to log back in later with an outline of the method for this.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: Vector 2

Ok show me methid

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Malik

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Vector 2

Hi;

From what I can remember

the cross product, a × b, returns a vector that is perpendicular to both a and b

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: Vector 2

the cross product, a × b, returns a vector that is perpendicular to both a and b
How perpendicular what is methods of a.b and a×b etc plz tell

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Malik

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Vector 2

Hi;

I am getting:

So the vector that is perpendicular to both is -3 i + 6 j

If determinants are not what you like then MIF gives an explanation right here:

https://www.mathsisfun.com/algebra/vect … oduct.html

Unfortunately that explanation I am unable to understand so I use the determinant.

Incidentally, what is wrong with my answer? Why is it not satisfactory?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: Vector 2

I read all topic of vectors but not understand what is this in this link

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Malik

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: Vector 2

No explaination of determinant rules

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Malik

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Vector 2

Howdy;

Computing determinants is a thankless job and I have seen everyone, myself included make silly arithmetic mistakes and then watch in horror as the rocket exploded due to those mistakes. That is why I always use a computer to do them. My motto is, "let their rocket explode, better theirs than mine."

There was a funny incident on public tv here where someone tried to do a 4 x 4 determinant live on tv. She of course failed again and again.

There is a formula for them:

Formulas have little meaning we forget them in about a day or so. Methods, also have little meaning. But if you do a couple of examples with me right here you will remember it for a long time. Want to?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: Vector 2

Yup

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Malik

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Vector 2

Hi;

Let us do an easy one, we start with two vectors in component form.

<2,3,4> and <5,6,7>. We want to cross product them. What would you do first?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: Vector 2

How take cross product

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Malik

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Vector 2

Hi;

Call a = <2,3,4> and b = <5,6,7>

Use the formula I gave you:

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: Vector 2

21-24,20-14,12-15
-3,6,-3

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Malik

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Vector 2

That is very good, you got the right answer!

Now this one:

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: Vector 2

What is x

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Malik

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Vector 2

That means cross product.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: Vector 2

How take cross product

I Want concept also.

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Malik

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Vector 2

How take cross product

When you did <2,3,4> and <5,6,7> you took a cross product.

When I did your

Find a vector perpendicular to each of the vectors
A vector =2i+j+k
b vector =4i+2j-k

I took a cross product.

Use the formula.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: Vector 2

Now this one:
<3,1,5> x <8,4,3>
3-20,40-9,12-8
-17,31,4

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Malik

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Vector 2

Very good! Now you will do a tough one.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: Vector 2

Can u plz tell me concept of dot and cross product

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Malik

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Vector 2

Question 2
Find a vector perpendicular to each of the vectors
A vector =2i+j+k
b vector =4i+2j-k

That was your question. It asks for an answer not a theoretical discussion. I am showing you how to get a vector that is perpendicular to the other two. One question at a time.

But if you do a couple of examples with me right here you will remember it for a long time. Want to?

Yup

You did not do the problem I gave you... Please do that.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: Vector 2

But i dont know vectors so how i find perpendicular and also dont know this perpendicular question first i want know what is this .. thats not only question but also theory question  what i do with ans this also in my keybook but in exams mcqs and also conceptual question so what i do in exam

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Malik

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Vector 2

What do you mean how do you find a perpendicular vector? That is what I am showing you what to do.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.