You are Here: Home

# P3 vectors watch

1. How do I prove that a point lies on a line?
I don't know what to do...I'm not talking about a particular exercise but in general as I wanna know how....
2. (Original post by toxi)
How do I prove that a point lies on a line?
I don't know what to do...I'm not talking about a particular exercise but in general as I wanna know how....
I'm pretty sure you have to equate the coefficients of your i's j's and k's, then you should get λ=...
If the point lies on the line the value of λ should be the same in all 3 cases
3. (Original post by toxi)
How do I prove that a point lies on a line?
I don't know what to do...I'm not talking about a particular exercise but in general as I wanna know how....
ok so you have a line r=ai+bj+cj+Δ(di+ej+fk).
Now if a point P with position vector : xi+yj+zk lies on the line,then (a+Δd) would be equal to x,So find Δ.Now do the same for the j and k coefficients and u will find that the value of Δ would be the same for all of them.
4. (Original post by IntegralAnomaly)
ok so you have a line r=ai+bj+cj+Δ(di+ej+fk).
Now if a point P with position vector : xi+yj+zk lies on the line,then (a+Δd) would be equal to x,So find Δ.Now do the same for the j and k coefficients and u will find that the value of Δ would be the same for all of them.

ok i think ill re write this in another equation

assuming
r = 5i + 6j +2k + k(i + 2j + 3k)
and you are asked to prove that line 6i + 8j + 5k is on this equation
(bear in mind that im taking this numbers out of random)
kk..
now let k as 1
(this depends on the question...cause k can be anything...so you can use 2 or 3 or whatever depending on what line touches...im using 1 cause i need the sum of 5 + k = 6...thus k has to be one)

now if i let k as 1
r = (5+1)i + (6+2)j + (3+2)k
r = 6i + 8j + 5k (proven)
therefore,the line is in the equation

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: June 6, 2004
Today on TSR

### Congratulations to Harry and Meghan!

But did you bother to watch?

### Why are girls so attracted to tall guys?

Poll

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