You are Here: Home >< Maths

# Vector Equation watch

1. The points A(1,0), B(7,2) and C(13,7) are the vertices of a triangle.
The midpoints of the sides BC, CA and AB are L, M and N.
Find the vector equation of the lines AL

I got an answer of (1,0) + λ(3,2.5) by doing:
AL = OA + AL, however the book has an answer of (1,0) + λ(2,1), and i'm not sure how they got that answer.
2. (Original post by znx)
The points A(1,0), B(7,2) and C(13,7) are the vertices of a triangle.
The midpoints of the sides BC, CA and AB are L, M and N.
Find the vector equation of the lines AL

I got an answer of (1,0) + λ(3,2.5) by doing:
AL = OA + AL, however the book has an answer of (1,0) + λ(2,1), and i'm not sure how they got that answer.
L is the midpoint of BC. So its coordinate is (10,4.5). The vector AL is thus OL-OA = (9,4.5) = 4.5(2,1) which has direction (2,1).
3. (Original post by RDKGames)
L is the midpoint of BC. So its coordinate is (10,4.5). The vector AL is thus OL-OA = (9,4.5) = 4.5(2,1) which has direction (2,1).
Thank you mate for the help
4. (Original post by RDKGames)
L is the midpoint of BC. So its coordinate is (10,4.5). The vector AL is thus OL-OA = (9,4.5) = 4.5(2,1) which has direction (2,1).
For the vector equation for BM:
I did the same thing as for AL, which is BM = OM - OB, and i got an answer of (0,1.5) However the book says it should be (0,1)?

And for CN:
I got it as (-3,-2), but the book got it as (3,2) - does the negative make a difference?
5. (Original post by znx)
For the vector equation for BM:
I did the same thing as for AL, which is BM = OM - OB, and i got an answer of (0,1.5) However the book says it should be (0,1)?

And for CN:
I got it as (-3,-2), but the book got it as (3,2) - does the negative make a difference?
You can take out a factor of 1.5 and have the direction as (0,1)

The -ve doesnt make a difference as that's just going the other way. You can factor it out too.

In case you're wondering why we can do these, it's because if you end up with some vector equation then you can just move the common factor of 5 from the vector to combine it with the to give . But time is generally an unrestricted parameter so 5t will take all the values anyway just as t would on its own, so you may as well replace 5t back with t as it makes no difference.

### Related university courses

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: February 27, 2018
The home of Results and Clearing

### 2,206

people online now

### 1,567,000

students helped last year
Today on TSR

### University open days

1. SAE Institute
Animation, Audio, Film, Games, Music, Business, Web Further education
Thu, 16 Aug '18
2. Bournemouth University
Fri, 17 Aug '18
3. University of Bolton
Fri, 17 Aug '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