Question

find a vector function r(t) that, as t goes from -∞ to ∞, will generate the entire line through p = (-2, -3, 3) in the direction of v = <3, 3, 0>.
r(t) =
submit answer next item
answers

your answer score

01 - / 1

Explanation:

Step1: Recall line - vector function formula

The vector - function of a line passing through a point $\mathbf{r}_0=(x_0,y_0,z_0)$ and in the direction of a vector $\mathbf{v}=(a,b,c)$ is given by $\mathbf{r}(t)=\mathbf{r}_0 + t\mathbf{v}$, where $t\in(-\infty,\infty)$.

Step2: Identify $\mathbf{r}_0$ and $\mathbf{v}$

Here, $\mathbf{r}_0=(-2,-3,3)$ and $\mathbf{v}=(3,3,0)$.

Step3: Substitute values into the formula

$\mathbf{r}(t)=(-2,-3,3)+t(3,3,0)=(-2 + 3t,-3 + 3t,3+0t)$.

Answer:

$\langle - 2+3t,-3 + 3t,3
angle$