# Math Help - perpendicular vectors

1. ## perpendicular vectors

No idea how to do this, all I know is you need the dot product.
Find two vectors V1 and V2 whose sum is <-4,3,0>, where V1 is parallel to and V2 is perpendicular to <-3,-1,5>.

2. Originally Posted by jahichuanna
No idea how to do this, all I know is you need the dot product.
Find two vectors V1 and V2 whose sum is <-4,3,0>, where V1 is parallel to and V2 is perpendicular to <-3,-1,5>.
This is a truly messy and tedious problem.
Let $v_1=~\&~v_2=<\alpha a, \alpha b, \alpha c>$.
Then the perpendicular part gives $-3a-b+5c=0$.

From that you get four equations in four variables. Solve it.

3. Originally Posted by Plato
This is a truly messy and tedious problem.
Let $v_1=~\&~v_2=<\alpha a, \alpha b, \alpha c>$.
Then the perpendicular part gives $-3a-b+5c=0$.

From that you get four equations in four variables. Solve it.
I still have no idea where to go. I cant even get started. can you please guide me all the way through it?

4. Originally Posted by jahichuanna
I still have no idea where to go. I cant even get started. can you please guide me all the way through it?
Understand, I will not do this for you.
Here is the set up.
$\left\{ \begin{gathered} (\alpha + 1)a = - 4 \hfill \\ (\alpha + 1)b = - 1 \hfill \\ (\alpha + 1)c = 0 \hfill \\ - 3a - b + 5c = 0 \hfill \\ \end{gathered} \right.$

Solve for $a,~b,~c,~\&,\alpha$

Again, do not ask me to do it.

5. Originally Posted by Plato
Understand, I will not do this for you.
Here is the set up.
$\left\{ \begin{gathered} (\alpha + 1)a = - 4 \hfill \\ (\alpha + 1)b = - 1 \hfill \\ (\alpha + 1)c = 0 \hfill \\ - 3a - b + 5c = 0 \hfill \\ \end{gathered} \right.$

Solve for $a,~b,~c,~\&,\alpha$

Again, do not ask me to do it.
understood. but I'm not clear on how exactly you got those equations

6. Originally Posted by jahichuanna
understood. but I'm not clear on how exactly you got those equations
You do not understand the question. Do you?
In which case how do you expect to get any help?
I am done with this thread.

7. How does he not expect help..? You could help him understand the question of course...

Okay so I'm assuming you know how to do cross products.

Let $\vec{a} = \vec{V_1}$ and $\vec{b} = \vec{V_2}$ and $\vec{a} = $ and $\vec{b}=$

Then it says the sum of the two vectors is <-4,3,0>. so

$ = <-4,3,0>$

$a_1+b_1=-4$
$a_2+b_2=3$
$a_3+b_3=0$

Then it says the first vector is parallel to <-3,-1,5>, so we use the dot product: $\vec{b} \bullet <-3,-1,5> = 0$

$\vec{b} * <-3,-1,5> = 0$
$-3b_1-b_2+5b_3=0$

Now the cross product. The theory is that $\vec{a} \times <-3,-1,5> = \vec{0}$

Doing that will give you three more equations. Solve for $a_1$ for $a_2$ and $a_3$ for $a_2$. Finally, plug those values in the first 3 equations. Then, solve for $b_1$, $b_2$, and $b_3$ and plug into the equation we got from the dot product.