Equations of Lines in 3D

Let be the line represented by the symmetric equations

1. Find the point of intersection of and the plane .

2. Find the distance between and .

3. The acute angle between and the line

Linear Independence

Let be a finite vector space over the set of rationals, and be a linear transformation from to . Suppose and are vectors in such that

(i)

(ii)

(iii)

Suppose is nonzero. Show that and are linearly independent vectors.