Write in parametric form the equation of the line that is perpendicular to r=(2i + 4j) + (i - 2j)t and goes through (1,0)

Answer 1

1 i - 2 j slope = -2
our slope = -1/-2 = 1/2
vector direction = 2 i + 1 j
so
r = (1i +0j) + (2 i + j) t

Answer 2

I could also say the dot product of vector 1 and vector 2 is 0 if they are perpendicular

V1 = 1 i - 2 j
V2 = a i + b j

V1 dot V2 = a -2 b = 0
so no matter what t is, a = 2 b
V2 = 2 i + 1 j or 4 i + 2 j
or in general
V2 = (2 i + 1 j) t