Question

Find the plane through point P(4, -1, 9) containing the line

Answer 1

To find the plane through point P(4, -1, 9) containing the line, substitute the coordinates of P into the equation of a plane and find the direction vector of the line to determine the values of A, B, C, and D in the equation of the plane.

Step-by-step explanation:

To find the plane through point P(4, -1, 9) containing the line, we need to find the equation of the plane. We can use the equation of a plane, which is Ax + By + Cz = D. Since the plane contains point P, we can substitute the coordinates of P into the equation to find the values of A, B, C, and D.

1. Substitute the coordinates of P into the equation: 4A - B + 9C = D.
2. Find the direction vector of the line and use it to find the values of A, B, and C in the equation.
3. Substitute the values found in step 2 into the equation to get the equation of the plane.

The equation of the plane through point P and containing the line is Ax - y + Cz = D, where A, B, C, and D are the values determined in step 2.