Answer:
t=0
Step-by-step explanation:
r=<[tex]at^2[/tex]+1,[tex]t[/tex]>
by differentiating the r vector component by component
r' = <2at, 1>
Two vector are orthogonal when the dot product between them is zero, so:
r'·r=0
<[tex]at^2[/tex]+1,[tex]t[/tex]>·<2at, 1>=2[tex]a^2t^3[/tex]+2at+t=0
common factor
t([tex]2a^2t^2[/tex]+2a+1)=0
Then, the only real value for t is zero.
-> t=0
