Alrighty so this week we learned Chapter 12 Vectors and we had a take home test this weekend thats due tomorrow... Dont Forget!!! I am going to review what we learned in chapter 12.
Another word that means perdencidular is orthogonal.
To figure out if two vectors are orthogonal, find the dot product.
v1 . v2=x1 x2 + y1 y2
**the dot does not imply multiplication.
Properties
1. u . v= v . u
2. u . u= /u/^2
3. k(u . v)= (ku) . v
4. u . (v+w)= u . v+ u . w
u=(x1 , y2)
y=(x2 , y2)
z=(x3 , y3)
Prove the 4 Properties
if two vectors are orthogonal, the dot product=0
if two vectors are parallel, then x2/x1=y2/y1
Example:
u= (3,-6) v= (4,2) w= (-12, -6)
show that u&v are perpendicular and that v&w are parallel.
u . v= 3(4)+(-6)(2)=0
-12/4=-6/2
-3=-3
I could use some help with determinants like on our take home test where there is 4 columns and 4 rows.
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when you have a four by four you start by doing the same thing as you would with a three by three
ReplyDeletedelete row delete colomn
thus youl have
all -bll +cll -dll
but you now have three by threes
so then youll do a regular three by three again which will be multiplied by the letter outside of each set of three by three
it will look like this when youre done
a(ell) b(hll) c(kll)
fll ill Lll
gll jll mll
to work out you'd do just what you would do to complete solving for a three by three except before you multiply the answer of the three by three times the letter before it you have to multiply the letter before it by the letter outside the parenthesis
it will look like:
a(e)ll
a(f)ll
a(g)ll
etc
then youre done
i can show you some examples in class if necessary
its kind of hard to show on here.