suppose x=x0+tv and y=y0+sw are two parametric representations of the same line l in r^n
a. show that there are scalars t0 and s0 such that y0=x0+t0v and x0=y0+s0w
b. show that v and w are parallel
suppose x=x0+tv and y=y0+sw are two parametric representations of the same line l in r^n
a. show that there are scalars t0 and s0 such that y0=x0+t0v and x0=y0+s0w
b. show that v and w are parallel
Moogle wrote:
I took Linear Algebra at age 15.
I know attend MIT.
Yay.
"I KNOW attend MIT."
Great ! I hear they teach English courses there, you might want to consider taking one.
a=cos20
b
Therefore: b-a-b,b-i-bo,b-i bicky bi be bi bo bicky bi bo be
Ill give it a try..
first off you should define what 'x' and 'y' represent if they represent something(vectors,scalars,physical significancy..).
I could guess they have space units, so I assume 't and s' can not be vectors just in order to match the equation (otherwise you have to apply the scalar product and obtain therefore an scalar) lets named 'time' to represent something physical.
Therefore 'v' and 'w' are the velocities (just get them by derivating)
v=(dx/dt)
w=(dy/dt)
I didnt quite get what r^n means to you.
I will assume is just the real space in for example 3Dimension, ok? so R^3
Thus x=xo + tv
y=yo + sw (1)
where x=(x1,x2,x3), xo=(xo1,xo2,xo3),v=(v1,v2,v3)
y=(y1,y2,y3), ...... ......
we are trying to show that there are scalar verifying:
yo=xo + tov
xo=yo + sow (2)
you told us they are the same line, so we guess they just differ by a constant given by the parametric eq (but not a varying vector if you know what I mean) so:
a) x = y + cte therefore-->
xo + tv = yo + sw +cnt and substituting in (2):
yo - tv + sw+ cnt = yo + sow --->
sw -tv = sow +cnt' by idetifying terms
tv=cnt
sw=sow thus s=so means 's' can be expressed
as a constant and verify the proposed eq
same reasoning for the other eq.
b) to show they are parallel its enough to know (as supposed) they are speeds, so the derivative, will must have the same , so the same slope for the lines!, so they will be both parallels and will verify:
V.W = (V1, V2, V3).(W1, W2, W3)=
V1W1+V2W2+V3W3= MODULE(V).MODULE(W).COS(0º) (since they are parallel)
**I think this is probably not completely right since i didnt quite understand something on the parametric thing, but if somebody want to help me, will be fine. cheers.
hahaha sucks for you. I'm glad I don't have to take that shit. I took differential equations and I'm finished with all my math.