Question

Determine whether the linesr1(t) = ⟨0, 1, 1⟩ t⟨1, 1, 2⟩andr2(t) = ⟨2, 0, 3⟩ t⟨1, 4, 4⟩intersect. if so, find the point of intersection.

Answer 1

To determine if the lines r1(t) and r2(t) intersect, set their coordinates equal to each other and solve for t. If there is a solution, substitute it back into one of the original equations to find the point of intersection.

Step-by-step explanation:

To determine whether the lines r1(t) and r2(t) intersect, we need to find the values of t that make the equations for the lines equal to each other. We can set the x, y, and z coordinates of r1(t) equal to the x, y, and z coordinates of r2(t) and solve for t. Once we find the value of t, we can substitute it back into either equation to find the point of intersection. For example, let's set the x coordinates equal to each other:

0 + t(1) = 2 + t(1)

Simplifying this equation gives us t = 1.

Substituting t = 1 into either equation (let's use r1(t)) gives us the point of intersection: (0, 1, 1) + 1(1, 1, 2) = (1, 2, 3).