# Thread: Intersection of two vectors

1. ## Intersection of two vectors

Let a and b be non-zero vectors which are not parallel to each other. Further let OX = a + λb be the vector equation of a line l1 and let OX = 2a + μ(a + b) be the vector equation of a line l2 (with λ,μ real numbers). Express the position vector of the intersection of the two lines l1 and l2 in terms of a and b.
I dont really even know where to start with this? Id be really greatful for some help

2. Originally Posted by renlok
I dont really even know where to start with this? Id be really greatful for some help
Calculating the point of intersection:

$a + \lambda b=2a + \mu(a+b)$

$a + \lambda b=(2+\mu) a + \mu b$

That means:

$2+\mu = 1~\wedge~ \lambda = \mu$

I'll leave the rest for you.