Using vector calculus: Please, show as much detail possible (maybe even using mathematica)

Give the equation of a plane orthogonal to both planes:

2x + y - z = 4

4x - 2y + z = 7

(it's not unique)

Consider the hyperboloid x² + y² - z² = 1

The point (1, 0, 0) is on this hyperboloid. The line "l" with vector function realization: r(t) = <1, 0, 0> + t<0, 1, 1> lies completely on the hyperboloid.

Verify that all points of "l" are on the hyperboloid

Find a second line thru (1, 0, 0) that lies completely on x² + y² - z² = 1

The point (7, -4, 8) also lies on this function. Determine a line thru (7, -4, 8)