1. What is an equation of the plane with normal vector \(\langle 2,3,-5\rangle\) that contains the point \((1,-2,3)?\)
2. What is an equation of the plane that passes through the coordinates axes at \(x=4\) and \(y=-1\) and \(z=3?\)
3. What is an equation of the plane containing the three points \((1,-2,3)\) and \((3,1,-4)\) and \((0,7,1)?\) What are the coordinates of the points where this plane intersects the coordinate axes?
4. What is a parameterization of the line passing through \((1,-2,3)\) in the direction \(\langle 4,-3,2 \rangle?\) What are the coordinates of the points where this line crosses the coordinate planes?
5. What is a parameterization of the line passing through the points \((1,-2,3)\) and \((9,-8,-7)?\) What are the coordinates of the points where this line crosses the coordinate planes?
6. What is a parameterization of the line along which the planes \(x-2(y-3)+4(z+1)=0\) and \(3(x-1)+y-z=0\) intersect?
7. What are the coordinates of the point where the plane \(x-2(y-3)+4(z+1)=0\) and the line \(\langle 2,-6,1\rangle t + (1,4,4)\) intersect?