x Turn on thread page Beta
 You are Here: Home >< Maths

# Vectors help watch

1. I've been given the diagram shown.

O is the origin and the points A,B,C lie on the x,y,z axis respectively. The length of OA is 1 and angle ACO is 15 degrees and angle BCO is 30 degrees.

I found the length of OB and OC

OB is . And OC is;

.

I was then asked to find the coordinates of vectors AB AC and BC, I got those to be

.

.

.

The area of the triangle I found to be 19.3

I'm stuck on this final part of finding the coordinates of M where the normal to the plane of the triangle ABC meets the origin.

Any hints? Thanks.
Attached Images

2. (Original post by Music99)
I've been given the diagram shown.

O is the origin and the points A,B,C lie on the x,y,z axis respectively. The length of OA is 1 and angle ACO is 15 degrees and angle BCO is 30 degrees.

I found the length of OB and OC

OB is . And OC is;

.

I was then asked to find the coordinates of vectors AB AC and BC, I got those to be

.

.

.

The area of the triangle I found to be 19.3

I'm stuck on this final part of finding where the normal to the plane of the triangle ABC meets the origin.

Any hints? Thanks.
Sorry, I don't quite understand your question, is it to find the point where the normal passing through the plane and the origin intersects the plane ABC or...?
3. (Original post by Felix Felicis)
Sorry, I don't quite understand your question, is it to find the point where the normal passing through the plane and the origin intersects the plane ABC or...?
I have to find the coordinates of M, where the normal to the plane of the triangle ABC passes through the origin.
4. (Original post by Music99)
I have to find the coordinates of M, where the normal to the plane of the triangle ABC passes through the origin.
I'm sorry if I'm being really stupid here, but could you define M more clearly? xD Is it the point on the triangle connecting the normal from the plane ABC to the origin or is it the origin? If so, it's just (0,0,0)...
5. (Original post by Felix Felicis)
I'm sorry if I'm being really stupid here, but could you define M more clearly? xD Is it the point on the triangle connecting the normal from the plane ABC to the origin or is it the origin? If so, it's just (0,0,0)...
The point on the triangle connecting the normal of the triangle ABC to the origin.
6. (Original post by Music99)
The point on the triangle connecting the normal of the triangle ABC to the origin.
Ok, start by using the cross product to find the normal vector to the plane, to get the direction vector of the line. Then find the equation of the plane of ABC.

Now, you have a point on your normal line because it goes through the origin, so the equation of your normal line is:

This gives you a general point on your line for whatever multiple of lambda.

And note that when you have your plane equation in scalar product form, any point on the plane will satisfy so you can solve for lambda and find the point intersecting the plane
7. (Original post by Felix Felicis)
Ok, start by using the cross product to find the normal vector to the plane, to get the direction vector of the line. Then find the equation of the plane of ABC.

Now, you have a point on your normal line because it goes through the origin, so the equation of your normal line is:

This gives you a general point on your line for whatever multiple of lambda.

And note that when you have your plane equation in scalar product form, any point on the plane will satisfy so you can solve for lambda and find the point intersecting the plane
Ah okay makes sense, what do I cross with what though ?
8. (Original post by Music99)
Ah okay makes sense, what do I cross with what though ?
The direction vectors of either or
9. (Original post by Felix Felicis)
The direction vectors of either or
Ah okay I'll try it now, thanks .
10. (Original post by Felix Felicis)
The direction vectors of either or
So I just did the cross product and I get .

So then I have r= (0,0,0) + t(-1-2root3), but how would I solve for t as I don't know what x,y,z are. Sorry If I'm being dumb it's been a long day :P.
11. (Original post by Music99)
So I just did the cross product and I get .

So then I have r= (0,0,0) + t(-1-2root3), but how would I solve for t as I don't know what x,y,z are. Sorry If I'm being dumb it's been a long day :P.
Do you mean ? Your cross product should be a vector...I'm not sure if it's just the diagram's not to scale but I think that the point M shouldn't have a 0 'z' value so you should have some kind of component for the z-axis...but I dunno, I haven't done the question, do you have a mark scheme?

Like I said, that equation represents any point on the line for appropriate t-value. Just say that the t-value which puts a point from the origin to the plane is 't'. And what do you know about any point on a plane, ? Well so you can solve for t by using the dot product
12. Personally I do not think Jorj would approve of this...... hahahahha

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: April 21, 2013
Today on TSR

### Happy St Patrick's day!

How are you celebrating?

### Stay at sixth form or go to college?

Discussions on TSR

• Latest
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

## Groups associated with this forum:

View associated groups
Discussions on TSR

• Latest

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE