Question

Determine the vector and parametric equations of the plane that has x, y and z -intereepts {3}/ {2},-1 , and 3 , respectively.

Answer 1

The vector equation of the plane is r = a + s(3i) + t(-1j) + u(3k), and the parametric equations of the plane are x = 3s, y = -1 - t, and z = 3u.

Step-by-step explanation:

To determine the vector equation and parametric equations of a plane, we can use the intercepts given. The intercepts are (3, 0, 0), (0, -1, 0), and (0, 0, 3).

The vector equation of the plane is r = a + s(3i) + t(-1j) + u(3k), where a is any point in the plane and (3i), (-1j), and (3k) are the direction vectors along the x, y, and z axes respectively.

The parametric equations of the plane are x = 3s, y = -1 - t, and z = 3u, where s, t, and u are parameters.