Find a plane through the points (2, – 3,5), (3,5,5), (6, 7,5) Preview
Find the equation for the plane through the points Po(-2, -3,5), Q,(1,4, - 3), and R. (2. - 3. - 4). The equation of the plane is - 63x - 5y - 28z =1. (Type an equation.)
(6 pts.) Find the equation of the plane passing through the point (12,-3,5) and parallel to u=(4,4,0) and v = (3,-1,6).
3. Determine plane equation passing through points A(3,1, -1), B(2, 3, 4), C(-2, -3,5) Show calculation steps clear and cleanly.
Find the equation for the plane through the points Po(2,-2,4), Qo(-5,5,-1), and Ro(2,-1,-2). The equation of the plane is (Type an equation.) Find the equation for the plane through the points Po(2,-2,4), Qo(-5,5,-1), and Ro(2,-1,-2). The equation of the plane is (Type an equation.)
2. (5 points) (a) Find a vector perpendicular to the plane through the points A(0, -2,0), B(4,1, -2) and C(5,3,1). (b) Find an equation of the plane through the points A, B, and C. (b) Find the area of the triangle ABC.
2. (5 points) (a) Find a vector perpendicular to the plane through the points A(0, -2,0), B(4,1, -2) and C(5,3,1). (b) Find an equation of the plane through the points A, B, and C. (b) Find the area of the triangle ABC.
Find an equation for the plane through the points (4,3,5), (1,0,-1), (0,2,-2). The Plane is?
2. Let P(2, 2), Q(3,5) and R(4,3) be three points in the xy plane. (a) Determine the vectors a = PO, b =PŘ, and c =RQ and draw them on the xy plane below. (b) Calculate a - b and compare it to c. What do you notice? Explanation? R 2
Given the data points (-3,5),(-2,5),(-1,3), (0, 1) (a) Find the interpolating polynomial passing through these points. (b) Using your polynomial from (a), evaluate P(1). (c) This polynomial interpolates the function f(x) = 24. Find an upper bound for the approximation in part (b).
(6 points) Use the network shown below to answer the following questions: (7,5) (8,8) (5,3) s (6,0) T (3,3) (4,3) (3,0) (5,0) B (4,0) D (a) What is the current flow through this network? (b) Find the last remaining augmenting semipath within this network and determine by how much the flow can be augmented from that path.