Finding the value of a and intersection point of two lines in vector form

[lemon]

1. Given that the two lines r1 and r2 intersect, find the value of a and hence determine the point of intersection.
r1=i+9j-3k+landa(i+j-k)
r2=4i+ak+mew(6i+5j+k)

Homework Equations

3. I'm a little lost with this one. Do I need to rewrite in parametric form and then cartesian form then compare i and j components. Then find values of mew and landa. Then use r1 and plug in landa value and solve for point of intersection?

 

[lemon]

Using this technique I get a=-6
and point of intersection is -52i-45j-12k

Could somebody check this please?

 

[Mark44]

At a point of intersection, r₁ = r₂,
so <1 + s, 9 + s, -3 -s> = <4 + 6t, 0 + 5t, a + t>
(I have dispensed with "landa" (lambda) and "mew" (mu), and replaced them with s and t.)
For two vectors to be equal, their corresponding components must be equal.

The value I get for a is 78.

 

[lemon]

yes thank you. I made a mistake in my layout. I have 78 now.
and
4i+ak-12(6i+5j+k)
4i+78k-72i-60j-12k
which gives -34i-30j+33k