Consider the parabola r(t)equalsleft angle at squared plus 1 comma t right angle, for minusinfinityless thantless thaninfinity
, where a is a positive real number. Find all points on the parabola at which r and Bold r prime are orthogonal?
1 answer:
Answer:
t=0
Step-by-step explanation:
r=<+1,>
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
<+1,>·<2at, 1>=2+2at+t=0
common factor
t(+2a+1)=0
Then, the only real value for t is zero.
-> t=0
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