# S.O.S. Mathematics CyberBoard

Your Resource for mathematics help on the web!
 It is currently Tue, 21 May 2013 23:37:51 UTC

 All times are UTC [ DST ]

 Page 1 of 1 [ 4 posts ]
 Print view Previous topic | Next topic
Author Message
 Post subject: A few questions - PlanesPosted: Sun, 1 Jun 2003 05:31:54 UTC
 Member

Joined: Mon, 26 May 2003 01:25:40 UTC
Posts: 32
Just a few questions. Muchly thanx for the help in advance.

Show that the lines x-1=(y-2)/2=z+3 and x+1=y-3=2z+5 are coplanar and find the equation of the plane which contains them.

Also...

Q is any point in the plane Ax+By+Cz = D
d is the distance from P(x1, y1, z1) to the given plane.

Explain why d = (l QP * n l)/l n l

(where * means dot product and l are modulus signs, oh and n is the normal vector)

Thanx guys

Top

 Post subject: Re: A few questions - PlanesPosted: Sun, 1 Jun 2003 06:12:23 UTC
 S.O.S. Oldtimer

Joined: Mon, 19 May 2003 07:15:29 UTC
Posts: 204
Location: Los Angeles
Way Below Xero wrote:
Show that the lines x-1=(y-2)/2=z+3 and x+1=y-3=2z+5 are coplanar and find the equation of the plane which contains them.

Line A:
Line B:

Line A:

Line B:

In both line A and B:

This is the plane which contains both lines.

_________________
My thoughts on Pi:
How I need a drink, alcoholic of course, drunk for happy feelings ...

Top

 Post subject: continuedPosted: Mon, 2 Jun 2003 01:56:52 UTC
 Member

Joined: Mon, 26 May 2003 01:25:40 UTC
Posts: 32
Thanx andy

Could someone have a look at the second bit as well???

(The proof)

Top

 Post subject: Posted: Mon, 2 Jun 2003 02:46:43 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Mon, 19 May 2003 19:55:19 UTC
Posts: 7949
Location: Lexington, MA
Hello, Way Below Zero!

This is a "projection" problem - which has a standard proof.
I'll modify it for this particular problem.

Draw a horizontal line (the plane).
Draw a vector upward from the line (the normal n) through point P.
Let the foot of the perpendicular be R. Then |PR| = d.
On the horizontal line select point Q, and draw QP.

Let angle QPR = .

In the right triangle:

The angle between QP and n is given by:

So, we have:

Top

 Display posts from previous: All posts1 day7 days2 weeks1 month3 months6 months1 year Sort by AuthorPost timeSubject AscendingDescending
 Page 1 of 1 [ 4 posts ]

 All times are UTC [ DST ]

#### Who is online

Users browsing this forum: No registered users

 You cannot post new topics in this forumYou cannot reply to topics in this forumYou cannot edit your posts in this forumYou cannot delete your posts in this forum

Search for:
 Jump to:  Select a forum ------------------ High School and College Mathematics    Algebra    Geometry and Trigonometry    Calculus    Matrix Algebra    Differential Equations    Probability and Statistics    Proposed Problems Applications    Physics, Chemistry, Engineering, etc.    Computer Science    Math for Business and Economics Advanced Mathematics    Foundations    Algebra and Number Theory    Analysis and Topology    Applied Mathematics    Other Topics in Advanced Mathematics Other Topics    Administrator Announcements    Comments and Suggestions for S.O.S. Math    Posting Math Formulas with LaTeX    Miscellaneous