Question

Test in 2 hours, help with matrix

Answer 1

Above is the question, below is my work.

Answer 2

Ill just type my work out, my phone is not sending the picture through.

Answer 3

i can't see your work i only see the question parts

Answer 4

I remember the tangent is the normalized velocity vector.

Answer 5

\[T(t)=<-\frac{ 2 }{ 3 }\sin(t), \frac{ 2 }{ 3 }\cos(t), \frac{ \sqrt{5} }{ 3 }>\]
\[N(t)=<-\frac{ 4 }{ 9 }\cos(t), -\frac{ 4 }{ 9 }\sin(t), 0>\]

Im trying to find the equation of the oscillating plane which is \[T(t) X N(t)\]

but its getting messy because I have to foil out the last matrix and it doesnt seem correct

Answer 6

remind me, how do you find N ?

Answer 7

\[N=\frac{ T'(t) }{ ||r'(t)|| }\]

Answer 8

for part d, I assume we use t=0 in both T and N ?

Answer 9

so we find the cross of <0, 2/3, sqr(5)/3> X < -4/9 , 0 , 0>

Answer 10

thats where I was confused