Question

what are parametric equations direction numbers, symmetric equations, and normal vectors ? what are parametric equations direction numbers, symmetric equations, and normal vectors ? @MIT 18.02 Multiva…

Answer 1

and what are they used to find

Answer 2

PARAMETRIC EQUATIONS are used to find points on a region
they are also used to find velocity and acceleration
they are in the form x= x(t), y=y(t), z=z(t)
in order to convert two parametric equations to one,
1. if you can, elimate t, if not good luck {by solving for t}
2.sub expression into other

thhhhhhhheeeeere yaaaaaaaaaa goooooo

Answer 3

positive direction of a vector is from p1-p2
negative direction of a vector is from p2-p1
Direction Numbers are any 3#s proportional to direction cosiness of a line seg(vector)
Direction angles
they are the angles that P1P2 (vector) make with pos x, y,z coord axis[alpha, beta, weird y resp.]
Direction cosines - cosines of direction angles
using two points P1P2
ex. cos alpha= xsub2-xsub1 , cos beta =ysub2 -ysub1, cos weird y=zsub2-zsub1 {separately each is divided by d [distance bewteen P1P2=length-magnitude
note that cos ^2alpha +cos^2beta+cos^2 weird y=1 , lambda, curs u, curs,v resp.

Answer 4

symmetric equations
a line needs a pt and a direction *note should be at top
you can get xyz intercepts from equation of plane by setting the other two variables =o aand
you can also get perpendicular -orthogonal-normal direction by taking the cooeffiec of x y and z from equation of plane
*note parallel vectors r usually given, perp orth norm. u have to find
take pt and direction plug into r(t)[vector equation]=rsub 0(point) + t *v(direction from xyz coeff. of eqaution of plane)
*note parametric equations are derived
[find symmetricla equations, or you can find points on the line by plugging in any number]
for symmet equations solve each paramtetric equation for t thus symmetrical equations= each t parameter = to each
you can use symmetric equations to find where a line intersects a certain plane by setting the left out variable =0 and solving for the plane variables, giving you a point( ) where left out=0
to show that lines are skew given only parametric equations
refer to parametric equation the corresponding t variables are vectors <>
using these vectors the vectors will be parallel if scalar multiple sof eahc other. the vectors will intersect if you can take line 1 parametric equationx=line 2 parametric eqauationx, same with remainding parametric equations , then solve for s and t and plg into remaining l1=l2 param. equation. if you obtain a true statement they intersect.
those lines are perpendicular orth normal if dot prodct =0
*check by subbing in any unit vector.
function of two variables is skew-symmetric if f(y, x) = −f(x, y). The property implies f(x, x) = 0 (except in fields of characteristic two).