Steps for

Tutorial $3$

Compute the unit tangent vector and principal unit normal vector for each of the following vectors.

a

b$)r(t)=$

c$)r(t)=$

$[Ans$: ; $b$

Evaluate

a$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}dt$

b$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}dt$

c$){\displaystyle \underset{1}{\overset{4}{}}}($:$\sqrt[\phantom{2}]{t},5$:$)dt$

d

$[$Ans: a b c d$)<mtext></mtext><mi>[</mi>$:$4ln3,1-e^{-2},e^2+1>\}$

Find the arc length of the following curves.

a

b$),r(t)=\sqrt[\phantom{2}]{2t}i+e^{t}j+e^{-t}k,0t1.$

$[$Ans: a$)20\sqrt[\phantom{2}]{29},$ b$)e-e^{-1}]$