Consider the vector-valued function r\left(t\right)=3t^2i+\left(t-1

chanyingsauu7 2021-11-16 Answered
Consider the vector-valued function \(\displaystyle{r}{\left({t}\right)}={3}{t}^{{2}}{i}+{\left({t}-{1}\right)}{j}+{t}{k}\). Write a vector-valued function u(t) that is the specified transformation of r. A horizontal tra
ation one unit in the direction of the positive x-axis

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Expert Answer

Sue Leahy
Answered 2021-11-17 Author has 25 answers
Step 1
The given function is \(\displaystyle{r}{\left({t}\right)}={3}{t}^{{2}}{i}+{\left({t}-{1}\right)}{j}+{t}{k}\)
Step 2
Here \(\displaystyle{x}{\left({t}\right)}={3}{t}^{{2}},{y}{\left({t}\right)}={t}-{1},{z}{\left({t}\right)}={t}\)
A horizontal tra
ation one unit in the direction of the positive x-axis gives the function x(t) as,
\(\displaystyle{x}{\left({t}\right)}={3}{t}^{{2}}+{1}\)
Thus, \(\displaystyle{r}{\left({t}\right)}={\left({3}{t}^{{2}}+{1}\right)}{i}+{\left({t}-{1}\right)}{j}+{t}{k}\).
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