Question

An implicit equation for the line through (2,-1) normal to the vector<-3,3> is?

Answer 1

Okay, first you want to find the slope of the vector. Then you can find out the slope of the line which is normal to it.

Answer 2

Is the slope -1?

Answer 3

implicit .... this sounds like its not going to be in slope intercept form is it

Answer 4

will it be a vector equation? r = p + v

or, x= ... ; y= ...

or maybe ax+by=c

Answer 5

I believe implicit means the same as general which is ax + by = c.

Answer 6

we can live with that :)

Answer 7

yes, -1 is the slope of the given vector; do you recall the definition for a normal vector?

Answer 8

A normal vector.. N dot x = N dot p?

Answer 9

hmmm, i was looking more for: perpendicular

Answer 10

the slope of a vector and its normal vector are 90 degree to each other; at right angles; orthogonal .... perpendicular

Answer 11

if you know the slope of the given vector to be -1; what property of perp slopes gives us the slope of the normal vector?

Answer 12

the negative reciprocal?

Answer 13

if the given slope is m1
and the perp slope is m2

then m1 * m2 = -1

yes, the negative reciprical is a good description of it :)

Answer 14

so the slope of our line is the negative reciprical of -1; which is 1 correct?

and when given a point and a slope; we can utilize the point slope form of a line and simplify it into the ax+by=c form from there

Answer 15

Okay, so that's what I thought.. so how can I write it in ax + by = c form?

Answer 16

when we have a point, (a,b); and a slope, m; the point slope form of the line takes the form:\[y-b=m(x-a)\]we can push this around to get\[y-b=mx-ma\]\[-mx+y=-ma+b\]and since some text dont like a negative out front we might have to clean it up by multiplying thru by -1

Answer 17

\[-(1)x+y=-(1)(2)+(-1)\]
\[-x+y=-2-1\]
\[-x+y=-3\]
\[x-y=3\]

Answer 18

Raph is just showing off :)

Answer 19

So he isn't doing what is supposed to be done for this problem?

Answer 20

dunno, there wasnt a method asked for

Answer 21

I know how to out find it, but Raphael's method almost seems like the intended method.

Answer 22

lol; yeah, it is pretty sweet; almost feels like cheating

Answer 23

@amistre64 lol

Answer 24

@RaphaelFilgueiras What inspired the (x-2, y+1) vector?

Answer 25

if the point x,y lie in line then the vector(x-2,x-(-1) will lie in line too

Answer 26

@RaphaelFilgueiras Can you elaborate? How do you know?

Answer 27

Hmmm I know the vector components will remain proportional to each other...

Answer 28

That proportion will be the slope by design.

Answer 29

@wio get it?

Answer 30

Yeah I get it.