Please help with these 4 Vector Questions

Hi,

I am struggling with these. Can you go through them with me:


Many Thanks

Can you do any of them?

For starters, how do you check whether a point is on a line?

For question A:

I brought B (1,1,3) over to make it:

(-4,-6,2) + λ (4,6,-2)

So λ = -1 because satisfies in each case. Therefore B lies on the line

I can't do any of the other 3.

For question b I tried the simultaneous equation method to make these 3:

-3+4λ = -7-3μ
-5+6λ = 2+2μ
5-2λ = -2μ

But I couldn't isolate either Lambda or Mu

For question A:

I brought B (1,1,3) over to make it:

(-4,-6,2) + λ (4,6,-2)

So λ = -1 because satisfies in each case. Therefore B lies on the line

I can't do any of the other 3.

For question b I tried the simultaneous equation method to make these 3:

-3+4λ = -7-3μ
-5+6λ = 2+2μ
5-2λ = -2μ

But I couldn't isolate either Lambda or Mu

Just pick the top 2 equations and solve them simultaneously, then verify the result by plugging lambda and mu into the third equation to see if it's satisfied.

Pick two equations out of the three, solve them and then check that the values work in the third equation.

I suspect I've done something wrong here as I can't get it to satisfy

Finding the coordinate of the intersect: I don't think this is gonna work...