Question

Describe the object in R^4 that is represented by the vector equation and find parametric equations for it? for example like (x_1, x_2, x_3, x_4) =(-1,0,4,2) + t_1(-3,5,- 7,4) + t_2(6,3,-1,2)

Answer 1

Like how do you know when its a line and when its a plane

Answer 2

If u have vector p and li vectors v, w in R^n then

y = tv + sw + p is a plane (the li vectors guarantee a 2D object)

If y = (y1,y2....yn) (ditto v,w,p) ->

y1 = tv1 +sw1 +p1, y2=tv2+sw2+p2,etc (parametric)

(Compare y = tv +p for a line)