3D Vector Word Problem Help

**Morphayne** · June 3rd 2008, 12:42 PM

Problem:

Determine the value of m so that the vectors u=[4, -2, 6] and v=[6, m, 9] are:

a) Parallel
b) Perpendicular

Answers: a) -3
b) 39

Comments:

Please help me!

**Moo** · June 3rd 2008, 12:46 PM

Hi !

Originally Posted by Morphayne

Problem:

Determine the value of m so that the vectors u=[4, -2, 6] and v=[6, m, 9] are:

a) Parallel
b) Perpendicular

Answers: a) -3
b) 39

Comments:

Please help me!

If two vectors are parallel, there exists a real number x, different to 0, such that :
$\vec{u}=x \vec{v}$

So seeing that $4={\color{red}\frac 23} \cdot 6$ and $6={\color{red}\frac 23} \cdot 9$ , can you set up a relation between -2 and m ?

------------------------------
Now, if two vectors are perpendicular, this means that the dot product is 0.
For two vectors : $u=\begin{pmatrix} u_1 \\ u_2 \\ u_3 \end{pmatrix}$ and $v=\begin{pmatrix} v_1 \\ v_2 \\ v_3 \end{pmatrix}$ , their dot product is :

$u_1v_1+u_2v_2+u_3v_3$

So here, what is the dot product of u and v ? Deduce the value of m ?

**galactus** · June 3rd 2008, 12:47 PM

The vectors are perpendicular when the dot product is 0.

$4(6)+(-2)m+6(9)=0$

Solve for m

**Morphayne** · June 3rd 2008, 01:00 PM

Originally Posted by Moo

If two vectors are parallel, there exists a real number x, different to 0, such that :
$\vec{u}=x \vec{v}$

So seeing that $4={\color{red}\frac 23} \cdot 6$ and $6={\color{red}\frac 23} \cdot 9$ , can you set up a relation between -2 and m ?

------------------------------
Now, if two vectors are perpendicular, this means that the dot product is 0.
For two vectors : $u=\begin{pmatrix} u_1 \\ u_2 \\ u_3 \end{pmatrix}$ and $v=\begin{pmatrix} v_1 \\ v_2 \\ v_3 \end{pmatrix}$ , their dot product is :

$u_1v_1+u_2v_2+u_3v_3$

So here, what is the dot product of u and v ? Deduce the value of m ?

I don't quite understand the explanation of the parallel part.

**Moo** · June 3rd 2008, 01:05 PM

Originally Posted by Morphayne

I don't quite understand the explanation of the parallel part.

There is a constant ratio between each coordinates of the two vectors, if they are parallel

Between 4 and 6, between -2 and m and between 6 and 9.

That is to say : $\frac 46=\frac{-2}m=\frac 69=x$ (the one I defined above

)

I hope this helps :x

**Morphayne** · June 3rd 2008, 01:29 PM

Could I get away with doing this:

-2/m=2/3

m=3(-2)/2

m=-3/1

m=-3

And BTW, is there a tutorial on how to use that fancy math text?

**Moo** · June 3rd 2008, 01:36 PM

Originally Posted by Morphayne

Could I get away with doing this:

-2/m=2/3

m=3(-2)/2

m=-3/1

m=-3

And BTW, is there a tutorial on how to use that fancy math text?

This is exactly what you have to do

For this fancy math text, see this section : http://www.mathhelpforum.com/math-help/latex-help/, especially this thread : http://www.mathhelpforum.com/math-he...-tutorial.html

**Morphayne** · June 3rd 2008, 01:48 PM

Moo, do you mind helping with one more? I posted it a short while back and I didn't understand the reply because the person was using techniques that I haven't even studied yet.

http://www.mathhelpforum.com/math-he...blem-help.html

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