Question

Find the equation of the plane through the three points (1,6,−10),(−6,−1,−5) and (−4,7,0). Enter your answer in the form ax+by+cz=d e.g 2x−3y+4z=10 will be entered as 2∗ x−3∗ y+4⁸z=10. Equation of the plane is:

Answer 1

To find the equation of the plane passing through three points, we use the steps: write down the coordinates of the three points, find two vectors that lie on the plane, take the cross product of the two vectors to find the normal vector, and substitute one of the points into the equation.

Step-by-step explanation:

To find the equation of the plane passing through three points, we can use the following steps:

1. Write down the coordinates of the three points given: (1, 6, -10), (-6, -1, -5), and (-4, 7, 0).
2. Find two vectors that lie on the plane by subtracting one point from another. For example, vector AB can be found by subtracting the coordinates of point A from the coordinates of point B.
3. Take the cross product of these two vectors to find the normal vector to the plane. This normal vector will be the coefficients of the variables in the equation of the plane.
4. Finally, substitute any of the three points into the equation of the plane to find the constant term.

So the equation of the plane that passes through the given three points is -5x + 29y - 26z = 20.