find vector equation of a hyperplane in $\mathbb R^4$ from scalar equation

Question

How would I go about finding a vector equation of a hyperplane $$3x_1+x_2-2x_3+4x_4=5$$

I know I need to find 3 vectors and another vector that shifts from the origin in the form $$r\vec{a}+s\vec{b}+t\vec{c}+\vec{d}$$

Answer 1

Hint: Take $x_1,x_3,x_4$ to be free variables. Then,

$$x_1=x_1$$

$$x_2=5-3x_1+2x_3-4x_4$$

$$x_3=x_3$$

$$x_4=x_4$$

Now write this in vector notation.