Question

Determine whether the line (1 – t, 2+2t, 1 – 3t) is parallel, orthogonal, or neither to the given plane. 1. bl (enter a, b, or c) a (1 – t, 2+2t, 1 – 3t) is parallel to the plane x + 2y +z = 9. b (1 – t, 2 + 2t, 1 – 3t) is orthogonal to the plane x + 2y +z = 9. c neither 2. с (enter a, b, or c) a (1 – t, 2+2t, 1 – 3t) is parallel to the plane x+y+z= -1. b (1 – t, 2+2t, 1 – 3t) is orthogonal to the plane x+y+z= -1. c neither

Answer 1

The line (1 − t, 2+2t, 1 − 3t) is neither parallel nor orthogonal to the plane x + 2y + z = 9.

Step-by-step explanation:

To determine whether the line (1 – t, 2+2t, 1 – 3t) is parallel, orthogonal, or neither to the given plane x + 2y +z = 9, we need to compare the direction vector of the line to the normal vector of the plane.

The direction vector of the line is (−1, 2, −3) and the normal vector of the plane is (1, 2, 1).

To determine if they are parallel, we can check if the direction vector is a scalar multiple of the normal vector. If it is, the line is parallel to the plane. If not, it is neither parallel nor orthogonal.

In this case, the direction vector (-1, 2, -3) is not a scalar multiple of the normal vector (1, 2, 1). Therefore, the line (1 − t, 2+2t, 1 − 3t) is neither parallel nor orthogonal to the plane x + 2y + z = 9.