# Dot and Scalar Product

• Sep 9th 2008, 07:30 PM
Elite_Guard89
Dot and Scalar Product
I have been lost in this forever due to missing the lecture, but does anybody know how to do this? Thank you for the help if you can.
a=3.0i+3.0j-2.0k
b=-1.0i-4.0j+2.0k
c=2.0i+2.0j+1.0k
The question is: a(dot)(axb)=?

Any help would be appreciated.
• Sep 9th 2008, 07:35 PM
Chris L T521
Quote:

Originally Posted by Elite_Guard89
I have been lost in this forever due to missing the lecture, but does anybody know how to do this? Thank you for the help if you can.
a=3.0i+3.0j-2.0k
b=-1.0i-4.0j+2.0k
c=2.0i+2.0j+1.0k
The question is: a(dot)(axb)=?

Any help would be appreciated.

What you are asked to evaluate here is what is know as the scalar triple product.

$\displaystyle \bold a\cdot\left(\bold b\times\bold c\right)=\left|\begin{array}{ccc}a_x&a_y&a_z\\b_x& b_y&b_z\\c_x&c_y&c_z\end{array}\right|$

Try to evaluate $\displaystyle \left|\begin{array}{ccc}3&3&-2\\-1&-4&2\\2&2&1\end{array}\right|$

This will give you the desired answer.

I hope this helps! (Sun)

--Chris
• Sep 9th 2008, 07:42 PM
Elite_Guard89
Okay, then how would you do a(dot)(b+c)?
• Sep 9th 2008, 07:43 PM
o_O
Add the vectors b and c to get b + c. Then take the dot product of a and what you found?
• Sep 9th 2008, 07:50 PM
Elite_Guard89
I understand the b+c part, but I'm not sure on how you find the dot product of a and what (b+c) creates.
• Sep 9th 2008, 07:54 PM
Chris L T521
Quote:

Originally Posted by Elite_Guard89
I understand the b+c part, but I'm not sure on how you find the dot product of a and what (b+c) creates.

When you take the dot product of a and this new vector (b+c), we get a scalar value. You multiply the like components together, and then add them all together. Note that $\displaystyle \bold i\cdot\bold i=\bold j\cdot\bold j=\bold k\cdot\bold k=1$

I hope this helps! (Sun)

--Chris
• Sep 9th 2008, 07:55 PM
o_O
Why not?

$\displaystyle \bold{b} + \bold{c} = (-1.0 + 2.0) \bold{i} + (- 4.0 + 2.0) \bold{j} + (2.0 + 1.0) \bold{k} = 1.0 \bold{i} - 2.0 \bold{j} + 3.0\bold{k}$

So: $\displaystyle \bold{a} \cdot (\bold{b} + \bold{c}) = (3.0 \bold{i} + 3.0 \bold{j} - 2.0 \bold{k}) \cdot (1.0 \bold{i} - 2.0 \bold{j} + 3.0\bold{k})$

Surely you can take the dot product of two vectors?
• Sep 9th 2008, 08:00 PM
Elite_Guard89
I would if I knew what a dot product was lol.
• Sep 9th 2008, 08:03 PM
Chris L T521
Quote:

Originally Posted by Elite_Guard89
I would if I knew what a dot product was lol.

The definition of the dot product:

If $\displaystyle \bold a=\left<a_x,a_y,a_z\right>$ and $\displaystyle \bold b=\left<b_x,b_y,b_z\right>$, the the dot product of a and b is:

$\displaystyle \bold a\cdot\bold b=a_xb_x+a_yb_y+a_zb_z$

I hope this helps! (Sun)

--Chris

w00t!!! My 8(Sun)(Sun)th post!! :D