smc-1196-45-Curves

Which diagram best shows the curve described by the position vector

`underset~r (t) = -5 text{cos}(t) underset~i + 5 text{sin}(t) underset~j + t underset~k` for `0 ≤ t ≤ 4 pi` ?

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`D`

Show Worked Solution

`text{By elimination}`

`text{Check graph coordinates for specific values of}\ t:`

`text{When} \ \ t = 4 pi \ , \ underset~r = -5 underset~i + 0 underset~j + 4 pi underset~k`

`-> \ text{Eliminate A and B}`

`text{When} \ t = pi/4 \ , \ underset~r = (-5)/sqrt(2) underset~i + 5/sqrt(2) underset~j + pi/4 underset~k`

`-> \ text{Eliminate C}`

`=>\ D`