A community for students.
Here's the question you clicked on:
 0 viewing
KatClaire
 3 years ago
Find the equation of the line of intersection of the planes with the equations 3x+4y+z=1 and 5x3z=5
KatClaire
 3 years ago
Find the equation of the line of intersection of the planes with the equations 3x+4y+z=1 and 5x3z=5

This Question is Closed

KatClaire
 3 years ago
Best ResponseYou've already chosen the best response.0Please help me work it out step by step :(

cherio12
 3 years ago
Best ResponseYou've already chosen the best response.2alright so you will have to use the cross product of the two normal vectors

KatClaire
 3 years ago
Best ResponseYou've already chosen the best response.0I did and I got 12i4j20k

cherio12
 3 years ago
Best ResponseYou've already chosen the best response.2hm...how'd u get yours?

amistre64
 3 years ago
Best ResponseYou've already chosen the best response.0practice makes perfect, good job so far cherio ;)

cherio12
 3 years ago
Best ResponseYou've already chosen the best response.2haha..gotta love calc =D..and ya i got 12i4j20k after i set it up right

cherio12
 3 years ago
Best ResponseYou've already chosen the best response.2so this is your direction vector i believe

cherio12
 3 years ago
Best ResponseYou've already chosen the best response.2now you need to to find a point that lie on this line

cherio12
 3 years ago
Best ResponseYou've already chosen the best response.2you can do this by taking your two planes and setting x,y, or z to zero and finding a point

KatClaire
 3 years ago
Best ResponseYou've already chosen the best response.0okay so if x=0 I get y=2/3 and z=5/3 , right?

cherio12
 3 years ago
Best ResponseYou've already chosen the best response.2yes, so for the next part you have to make a vector with that point (this will be dotted with the direction vector from before)

cherio12
 3 years ago
Best ResponseYou've already chosen the best response.2so typically for a line you just select the (x,y,z) to be your point (if anything doesn't make sense let me know) so you get (x0, y(2/3), z+(5/3)) as that vector

cherio12
 3 years ago
Best ResponseYou've already chosen the best response.2now i dot it with any scalar of the direction vector and get L=(x, y(2/3), z+(5/3))* t(12,4,20)

KatClaire
 3 years ago
Best ResponseYou've already chosen the best response.0Any reason why you do (x0,y(2/3),z+(5/3)? and you can't simplify that any more so that would be the answer?

cherio12
 3 years ago
Best ResponseYou've already chosen the best response.2well if you want to write in parametric or (something that starts with a s...symmetric?) you can simplify it a bit more..but as far at why x,y,z...um..i'll try to draw a picture.

amistre64
 3 years ago
Best ResponseYou've already chosen the best response.0in case i missed it, since the second plane has no y value, wouldnt it be simper to make y=0 in the first to solve for x,z ?

cherio12
 3 years ago
Best ResponseYou've already chosen the best response.2i just set x=0, so i didn't have to do substitution. other way works too

cherio12
 3 years ago
Best ResponseYou've already chosen the best response.2okay..not to try to explain the picture...

amistre64
 3 years ago
Best ResponseYou've already chosen the best response.0i get a common point of (2,0,5) :) but any common point will suffice

KatClaire
 3 years ago
Best ResponseYou've already chosen the best response.0well either way, I think I understand it more now! I was confused as to why the cross product was involved and what not. Thanks!!

amistre64
 3 years ago
Best ResponseYou've already chosen the best response.0crossing vectors created a new vector perp to both crossing 2 plane normals will get you a direction vector that is parallel to the line of insection
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.