[College - Calculus III] Vectors and Planes

**argo15** · 09-29-2009, 01:09 PM

Gosh, it might be a brain fart but I can't figure out how to do this.

Code:

Find a vector equation and parametric equations in t for the line through the point and perpendicular to the given plane. (P0 corresponds to t = 0.)
P0 = (4, 0, 7)
x + 2y + z = 6
v = ?i + ?j + ?k
x = ?
y = ?
z = ?

Answers or anything that might send me in the right direction would be awesome. =)

JKPolk · 09-29-2009, 01:12 PM

Have you tried taking the derivative with respect to each of the values and plugging in the intial conditions?

**argo15** · 09-29-2009, 01:17 PM

I don't think that is what he is looking for since this assignment is in the chapter before derivatives of vectors. Dot products or cross products are probably involved.

dooty_7 · 09-29-2009, 01:57 PM

I haven't done this for a while, so I hope what I say is not complete gibberish lol

For the equation of a plane, aren't the coefficients simply the normal (perpendicular) to the plane? If so then we have P0 = 4,0,7 and normal 1,2,2.

Leading us to get the general equation r = (4,0,7) + t(1,2,2)
so x = 4 + t
y = 2t
z = 7 + 2t

**foilman8805** · 09-29-2009, 02:03 PM

Quote:

Originally Posted by dooty_7

I haven't done this for a while, so I hope what I say is not complete gibberish lol

For the equation of a plane, aren't the coefficients simply the normal (perpendicular) to the plane? If so then we have P0 = 4,0,7 and normal 1,2,2.

Leading us to get the general equation r = (4,0,7) + t(1,2,2)
so x = 4 + t
y = 2t
z = 7 + 2t

Normal for the given plane is 1, 2, 1. I know it's a mistake though. You didn't mean to do that on purpose.

As a result the parametrics change to:

x = 4 + t
y = 2t
z = 7 + t

So, v is going to then be a substitution of the parametrics back into i, j, k form? I don't remember either lol...

EDIT: Yeah, I think v = (4 + t)i + (2t)j + (7 + t)k

**argo15** · 09-29-2009, 02:11 PM

Yeah, your right thank you =).

Answer was v= (4+t)i + (2t)j + (7+t)k

If I have any more issues I'll edit it in here. (math can be a bitch sometimes)

**foilman8805** · 09-29-2009, 02:13 PM

If you have more issues, bump the thread, otherwise we probably won't come back to look for it.

dooty_7 · 09-29-2009, 02:19 PM

lol brain fart on my part haha :P

09-29-2009, 01:09 PM	#1
argo15 FFR Veteran Join Date: May 2006 Age: 33 Posts: 1,863	[College - Calculus III] Vectors and Planes Gosh, it might be a brain fart but I can't figure out how to do this. Code: Find a vector equation and parametric equations in t for the line through the point and perpendicular to the given plane. (P0 corresponds to t = 0.) P0 = (4, 0, 7) x + 2y + z = 6 v = ?i + ?j + ?k x = ? y = ? z = ? Answers or anything that might send me in the right direction would be awesome. =)

09-29-2009, 01:12 PM	#2
JKPolk tool Join Date: Aug 2003 Location: satan Age: 37 Posts: 3,737	Re: [College - Calculus III] Vectors and Planes Have you tried taking the derivative with respect to each of the values and plugging in the intial conditions? __________________

09-29-2009, 01:17 PM	#3
argo15 FFR Veteran Join Date: May 2006 Age: 33 Posts: 1,863	Re: [College - Calculus III] Vectors and Planes I don't think that is what he is looking for since this assignment is in the chapter before derivatives of vectors. Dot products or cross products are probably involved.

09-29-2009, 01:57 PM	#4
dooty_7 Registered User Join Date: Jun 2005 Location: Hamilton Ontario Age: 36 Posts: 462	Re: [College - Calculus III] Vectors and Planes I haven't done this for a while, so I hope what I say is not complete gibberish lol For the equation of a plane, aren't the coefficients simply the normal (perpendicular) to the plane? If so then we have P0 = 4,0,7 and normal 1,2,2. Leading us to get the general equation r = (4,0,7) + t(1,2,2) so x = 4 + t y = 2t z = 7 + 2t __________________

09-29-2009, 02:11 PM	#6
argo15 FFR Veteran Join Date: May 2006 Age: 33 Posts: 1,863	Re: [College - Calculus III] Vectors and Planes Yeah, your right thank you =). Answer was v= (4+t)i + (2t)j + (7+t)k If I have any more issues I'll edit it in here. (math can be a bitch sometimes)

09-29-2009, 02:13 PM	#7
foilman8805 smoke wheat hail satin Join Date: Sep 2006 Location: LA baby Age: 35 Posts: 5,704	Re: [College - Calculus III] Vectors and Planes If you have more issues, bump the thread, otherwise we probably won't come back to look for it.

09-29-2009, 02:19 PM	#8
dooty_7 Registered User Join Date: Jun 2005 Location: Hamilton Ontario Age: 36 Posts: 462	Re: [College - Calculus III] Vectors and Planes lol brain fart on my part haha :P __________________

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