Question

(a) Find the point at which the given lines intersect. r = 1, 2, 0 + t 2, −2, 3 r = 3, 0, 3 + s −2, 2, 0 (x, y, z) =

(b) Find an equation of the plane that contains these lines.

Answer 1

The question requires solving for the point of intersection of two lines and then finding an equation for the plane containing those lines. The solution involves equalizing vector equations for the lines and using the intersection point and directional vectors to determine the equation of the plane.

Step-by-step explanation:

The student's question involves finding the point of intersection of two given lines and determining an equation for the plane containing those lines.

Firstly, find the point of intersection for the lines represented by r = (1, 2, 0) + t(2, -2, 3) and r = (3, 0, 3) + s(-2, 2, 0). This requires setting the vector equations equal to each other and solving for the parameters t and s.

Once the point of intersection is found, you can then find an equation of the plane. This involves using the point of intersection, and the direction vectors of the lines to find the normal vector of the plane. With the normal vector and the point of intersection, the plane's equation can be constructed using the general formula Ax + By + Cz = D, where (A, B, C) are the components of the normal vector and D is calculated based on the known point on the plane.