.
Find the cosine of the angle between and . For what values of is perpendicular to ? Parallel?
So
So or for .
But for I get . But this is undefined. So there are no values of for which and are parallel?
The vectors are perpendicular when t = 0.
They will be parallel when , where is a non-zero scalar.
So you need the following three equations to be satisfied:
... (1).
... (2).
... (3) (and this is equivalent to (1)).
From (2): . Sub this into (1):
which is no good since is a non-zero scalar.
So there is NO value of t such that the vectors are parallel,
Edit: unless the trivial solution of both vectors being the zero vector is granted.