How Do You Calculate the Length of AB When It Is Perpendicular to Line L?

[virtuosowanaB]

1. With respect to origin O, point A has position vector 30i - 3j - 5k. The line L passes through O and is parallel to the vector 4i - 5j -3k. The point B on L is such that AB is perpendicular to L. Find the length of AB. Find the position vector of B.

The Attempt at a Solution

Ok this is what i did.
Let L=y(4i -5j -3k)
Let b=x(4i -5j -3k)
Hence AB = [(4x-30)i (-5x+3)j (-3x+5)k]

Heres where i got quite stuck

Since AB is perpendicular to L. I tried AB.L=0
But I'm not very sure how do i solve this since there are 2 unknowns.

Ahh! Please help me out here! Thanks!

 

[HallsofIvy]

What is the equation of the plane containing A and having 4i- 5j- 3k as normal vector?

Where does the line L intersect that plane? That is point B.

 

[virtuosowanaB]

What is the equation of the plane containing A and having 4i- 5j- 3k as normal vector?

Where does the line L intersect that plane? That is point B.

Ahhh! Thanks! I missed out on the line that was on the next page of the book. Ok i can take it from here