Question

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Answer 1

@hartnn

Answer 2

Part c is you just take the dot product and that equals 0 right?

Answer 3

yup,part c procedure is correct ,u getting 0?

Answer 4

whats your vel vector?

Answer 5

yeah

Answer 6

veloctiry is <cos(t)/2, sqrt(3)/2 cos(t), -sin(t)>

Answer 7

so how about part d?

Answer 8

i think i got it,wait.

Answer 9

ok

Answer 10

ok,
\[||p^2 (t)||=constant=c\]
we know
\[||p^2(t)||=p(t).p(t)\]
so
\[\frac{d}{dt}p(t).p(t)=\frac{d}{dt}c=0\]
clear till here?

Answer 11

yeah

Answer 12

now using product rule:\[p(t).\frac{d}{dt}p(t)+\frac{d}{dt}p(t).p(t)=0\]
so \[2p(t)\frac{d}{dt}p(t)=0\]
implies
\[p(t)\frac{d}{dt}p(t)=0\]
now whats d/dt of p(t) ??

Answer 13

0?

Answer 14

sorry i forgot to put .(dot) in last 2 equations....

Answer 15

no,d/dt(p(t))=v(t)
so
\[p(t).v(t)=0\]
hence,the vel vector always perpendiculr to position vector....
got this?

Answer 16

Oh yeah. I understand now

Answer 17

glad to hear that :)

Answer 18

Thanks a lot