Question

Ques:1
1. Find r ′ and T for r = ht 2 , 1, ti
2. Find r ′ and T for r = hcos t, sin 2t, t2 i.

Answer 1

Solution;

1.Find r' and T for r=ht²,1,ti

r'=$\frac {d}{dt}$ r=2ht,0,i

T=$\frac{r'}{|r'|}$

$|r'|=\sqrt{(2ht)^2+0^2+i^2}=\sqrt{4h^2t^2-1}$

T=$\frac{2ht}{\sqrt{4h^2t^2-1}},0,\frac{i}{\sqrt{4h^2t^2-1}}$

2.Find r' and T for r=hcost ,sin2t ,t²i

r'=$\frac{d}{dt}$r=-hsint,2cos2t,2it

T=$\frac{r'}{|r'|}$

$|r'|=\sqrt{(-hsint)^2+(2cos2t)^2+(2it)^2}$ =$\sqrt{h^2sin^2t+4cos^2(2t)-4t^2}$

T=$\frac{-hsint}{\sqrt{h^2sin^2t+4cos^2(2t)-4t^2}},$ $\frac{2cos2t}{\sqrt{h^2sin^2t+4cos^2(2t)-4t^2}},$ $\frac{2it}{\sqrt{h^2sin^2t+4cos^2(2t)-4t^2}}$