Give Cartesian equations of the given hyperplanes: a. x = (1, 2) + t (3, 2) b. The plane

QUESTION:

Give Cartesian equations of the given hyperplanes:

a. \(\text { a. } \mathbf{x}=(-1,2)+t(3,2)\)

b. The plane passing through (1, 2, 2) and orthogonal to the line \(\mathbf{x}=(5,1,-1)+t(-1,1,-1)\)

c. The plane passing through (2, 0, 1) and orthogonal to the line \(\mathbf{x}=(2,-1,3)+t(1,2,-2)\)

d. The plane spanned by (1, 1, 1) and (2, 1, 0) and passing through (1, 1, 2)

e. The plane spanned by (1, 0, 1) and (1, 2, 2) and passing through \((-1,1,1)\)

f. The hyperplane in \(\mathbb{R}^{4}\) through the origin spanned by \((1,-1,1,-1),(1,1,-1,-1)\), and \((1,-1,-1,1)\).