wait wait!

I got values of μ and λ from the earlier post.

I compared i and j components and substituted back into equation 1

r1=[j+ak] +λ[2i+4j-3k]

r2=[4i+3j-6k]+μ[i+5j+k]

I need to rewrite these in parametric form

λi+(1+4λ)j+(3-3λ)k=(4+μ)i+(3+5μ)j+(6+μk)

comparing i components:

(1)

λ=4+μ

comparing j components:

(2)

1+4λ=3+5μ

λ=(2+5μ)/4

(1)=(2)

4+μ=(2+5μ)/4

16+4μ=2+5μ

μ=14

sub into (1)

λ=4+μ

λ=4+14

λ=18

Different values so the lines are skew

d) Find a value of a for which the lines intersect and state the coordinates of the point of intersection.

r1=2λi+(4λ+1)j+(a-3λ)k

r2=(μ+4)i+(5μ+3)j+(μ-6)k

I need to find the value of a for which the lines intersect and state the coordinates of point of intersection.

λ=18

μ=14

LHS a-3λ=μ-6

a-3(18)=14-6

a-54=8

a=62

r2=4i+3j-6k+μ[i+5j+k]

r2=4i+3j-6k+14[i+5j+k]

r2=4i+3j-6k+14i+70j+14k

18i+73j-8k

coordinates of point of intersection are:

(18, 73, -8)

How's that?