Final answer:
To find a vector v that is perpendicular to the plane through the points A=(-2,2,3), B=(-5,5,2), and C=(5,4,-2), you can use the cross product.
Step-by-step explanation:
To find a vector w that is perpendicular to the plane through the points A=(-2,2,3), B=(-5,5,2), and C=(5,4,-2), we can use the cross product. The cross product of two vectors A and B is given by the formula A × B = i((A2·B3) - (A3·B2)) - j((A1·B3) - (A3·B1)) + k((A1·B2) - (A2·B1)).
Using the points A=(-2,2,3), B=(-5,5,2), and C=(5,4,-2), we can find the vectors AB and AC. The cross product of AB and AC will give us the vector w that is perpendicular to the plane through the points.