Geometry help!

[phagist_]

Ok not sure if this is in the right section, but anyway.

I'm having trouble with this question

Find the distance from the point P(-1,2-1) from the line whose parametric equations are;



cheers!

[cara.mel]

I have answered in picture format because I fail at words:


If it doesnt make sense get someone else to clarify because I'm leaving pretty soon for work and won't be on FSN for probably 24 hours

[phagist_]

I can do it with Pythag.. but I'm having trouble finding the normal vector to project it onto.

Thanks anyway:)

[phagist_]

ahh nvm.. figured it out.. turns out I was using an equation wrong! it was doing my head in, haha.

[phagist_]

I really can't seem to get my head around geometry, I don't know why.

a) Find the vector equation of the plane through the points (2,-1,0) and (-5,-3,1) that is parallel to the line joining the points (3,5,-1) and (0,3,-2)

b) Find the parametric equations of the straight line through the origin that is perpendicular to this plane, and find where it intersects the plane.

-------------------------

but I am not sure by what it means 'vector equation'...

any help would be greatly appreciated,
cheers!

[Mao]

by vector equation, i hope they meant:


as for b), basically you need to find a point on that plane which perpendicularly projects a line through the origin. The line would follow the general vector equation . Since it is perpendicular to the plane, its "velocity" must be the normal vector, and since it goes through the origin, r(0)=(0,0,0). Hence, if we let the line be L,

[phagist_]

ah yep..any ideas on how to approach this?

[Mao]

so we know that the normal vector is <4,-10,8> (i hope), hence

hence, the cartesian equation for the plane is



subbing in any of those points would yield c=9

now, we also know that the equation for the line is

hence, subbing in the above vector for x,y,z:

[phagist_]

(2,-1,0) and (-5,-3.1) that is parallel to the line joining the points (3,5,-1) and (0,3,-2)

shit, just realised a typo should be (-5,-3,1).

and thanks a lot Mao.

[phagist_]

I was wondering, by vector equation.. could they also mean (x,y,z)+t(a,b,c)+s(d,e,f) ?

and if that was the case, then could use the vector joining (2,-1,0) and (-5,-3,1) and the vector joining (3,5,-1) and (0,3,-2).

To get

(2,-1,0) + t(-7,-2,1) + s(-3,2,1)

sorry if this is a dumb question, I just don't get this stuff and it's been a loooong day/

cheers

[Mao]

mmm it could

but i'm a little skeptical on using two parameters =P