You are Here: Home >< Maths

# Quickest way to find a point of intersection between two planes. watch

1. Hi guys.

Can anyone have a look at question 8 part a and help me understand how they have found a point of intersection between the planes, in the first method shown in the mark-scheme.

I managed to do the question but i converted to cartesian and eliminated variables. And my way looked much longer than the way in the mark-scheme.

I understand the cross product of the method i just need help with a quick way to find a point of jntersection thanks.

Thanks
2. You're given the equation of two planes, substitute some value (an easy one like x=0)
then solve the equations simultaneously to find a point of intersection. Remember to replace r by a general vector (x,y,z) and then work out the dot product. This will be a position on the line of intersection.

The vector normal to the 2 normals is parallel to the line of intersection. This is the direction vector.

So then its just position + direction.
3. (Original post by NotNotBatman)
You're given the equation of two planes, substitute some value (an easy one like x=0)
then solve the equations simultaneously to find a point of intersection. Remember to replace r by a general vector (x,y,z) and then work out the dot product. This will be a position on the line of intersection.

The vector normal to the 2 normals is parallel to the line of intersection. This is the direction vector.

So then its just position + direction.
Legend.

Now that you’ve said it I’m kicking myself that i didn’t realise i sooner.

Definitely much quicker than the method i used.

Thanks a bunch.
4. (Original post by Shaanv)
Legend.

Now that you’ve said it I’m kicking myself that i didn’t realise i sooner.

Definitely much quicker than the method i used.

Thanks a bunch.
No problem

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: March 10, 2018
Today on TSR

Get the low down

### University open days

• University of Exeter
Wed, 24 Oct '18
Wed, 24 Oct '18
• Northumbria University
Wed, 24 Oct '18
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams