Question

Show that vectors (1,-t,1+t) and (t,2+3t,6) are not parallel for any value of t?

Answer 1

parallel vectors have the same ratio to parts

1,3,5
3,9,15

all the rations are 1/3 since one is a scalar of the other

Answer 2

or we could try a dot product proof since

|u| |v| cos(a) = u.v

parallel in the same direction a=0; cos(0) = 1
parallel in opposite directions is a=pi; cos(pi) = -1

Answer 3

How do we know what the ratio is if we don't have t?