# Find a and b and the position vector of the point of intersection of C of $l_1$ and $l_2$

I asked a similar question to this yesterday, and I think I managed, however, I have a similar question but a bit different, if I understand this I think I'll manage to confirm the other one as well, so, how would one go about tackling this?

a) The points A and B have position vectors i-5k and 4i+3j+k, respectively. Find the equation of the line $$l_1$$ that passes A and B.

Basically, r=a+λ(b-a), which results to: $$i-5k+λ(3i+3j+6k)$$ Correct? or should I put my final answer as: $$i-5k+μ(i+j+2k)$$ Same answer but μ=3λ, would both be correct?

However, my main problem is this;

b) The line $$l_2$$ with vector question r=6i+j+ak+μ(2i+bj-k) intersects $$l_1$$ and is perpendicular to it. Find a and b, and the position vector of point of intersection C of $$l_1$$ and $$l_2$$.

A guideline on how to achieve it would be greatly appreciated.

## 1 Answer

Hint: In $$\vec r=\vec a+\lambda \vec b, \vec b$$ is the vector along the line. For two perpendicular vectors, the dot product has to be zero. The point of intersection can simply be solved by equating the i,j and k components of the vectors.