anonymous
  • anonymous
Determine a vector equation for the plane with Cartesian equation 3x-2y+z-6=0 .
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
terenzreignz
  • terenzreignz
First, you need its normal vector. Have you got it? ^_^
anonymous
  • anonymous
(3, -2, 1).. then?
terenzreignz
  • terenzreignz
That's right. Enclose it in <> so that you know it's a vector (and not referring to a point) And SPEAKING OF POINTS, you also need a point on the plane. It can be anything, but I suggest, you let x and y equal zero, and work out z.

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
oh ok:) x=y=0, the point is (0,0,6)
terenzreignz
  • terenzreignz
Good... Now, take a look at this 'plane' (pardon my poor drawing skills)|dw:1377969119221:dw| Are you LOOKING AT IT ?!
anonymous
  • anonymous
yes, it's good:)
terenzreignz
  • terenzreignz
Good.. now, say, this is your point (0,0,6)|dw:1377969171207:dw|
terenzreignz
  • terenzreignz
And THIS... is your NORMAL vector, <3,-2,1>|dw:1377969197698:dw|
terenzreignz
  • terenzreignz
|dw:1377969215443:dw|
terenzreignz
  • terenzreignz
Now, ANY point on the plane..., let's call it (x , y , z)...|dw:1377969249843:dw|
terenzreignz
  • terenzreignz
The vector IT makes with your known point, (0,0,6)... Which is... or...
terenzreignz
  • terenzreignz
|dw:1377969305747:dw|
terenzreignz
  • terenzreignz
This will ALWAYS be perpendicular to your normal vector:|dw:1377969349075:dw|
terenzreignz
  • terenzreignz
And thus, their DOT PRODUCT must always be...?
anonymous
  • anonymous
zero!!!! (^_^) yes i got it thank you very much!!!!!!!!!!
terenzreignz
  • terenzreignz
In fact, you didn't have to use the point (0,0,6) It could have been (0,1,8)
terenzreignz
  • terenzreignz
Or literally, any point that you know lies in that plane. Cheers ^_^
terenzreignz
  • terenzreignz
Typo... here's what it should really look like... \[\Large \left<3, -2, 1\right> \cdot \left=0\]

Looking for something else?

Not the answer you are looking for? Search for more explanations.