Question
Are the statements true or false? Give reasons for your answer.The line parameterized by $x=1, y=2 t, z=3+t$ is parallel to the $x$ -axis.
Step 1
To do this, we can take the derivative of each component with respect to the parameter $t$: $$\begin{cases} \frac{dx}{dt} = 0 \\ \frac{dy}{dt} = 2 \\ \frac{dz}{dt} = 1 \end{cases}$$ So, the direction vector of the line is $\begin{pmatrix} 0 \\ 2 \\ 1 Show more…
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