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.
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!
--Chris
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!
--Chris
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?
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!
--Chris
w00t!!! My 8th post!!