(3 points) Find an equation of the plane through the three points given: P = (0,3,0),...
1. Consider the points A(4,0,0), B(0,3,0),C(0,0,5), and P(1,2,8). a. Write the equation of the plane passing through the points A, B, and C. b. Write parametric equations of a line passing through point P and orthogonal to the plane described in part a. c. Find the exact distance between point and the plane described in part a.
Find the general equation and a vector equation of the plane that passes through the points p(1,2,4) Q(1,-1,6) R(1,4,8)
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.)
Find the volume of the tetrahedron in the first octant bounded by the coordinate planes and the plane passing through (5,0,0), (0,3,0), and (0,0,1) (0,3,0 5,0,0) The volume of the tetrahedron is. (Type an integer or a simplified fraction.) Find the volume of the tetrahedron in the first octant bounded by the coordinate planes and the plane passing through (5,0,0), (0,3,0), and (0,0,1) (0,3,0 5,0,0) The volume of the tetrahedron is. (Type an integer or a simplified fraction.)
Find an equation of the plane passing through the given points. (3, 4, -4), (3, -4,4), (-3, -4, -4)
Find the equation for the plane through the points Po(-5, -2,4), Q.(-3,-1,1), and Ro(-1,4,1). The equation of the plane is (Type an equation.)
Find an equation of the plane passing through the given points. (3, 4, -4), (3, -4,4), (-3, -4, -4) 7x - 6y - 7z - 25 = 0x
Find an equation of the plane passing through the given points. (3, 4, -4), (3, -4,4), (-3, -4,-4) 7x -6y - 72 – 25 = 0x
Find an equation of the plane passing through the given points. (3, 4, –4), (3, -4,4), (-3, -4, -4) Tx - 69 - 7z - 25 = 0 x
3. Consider the two planes, P and P2, where Pi is given by the general equation 2x y+2-5 and P2 passes through the points (0,0,-1), (3,2,4) and (2, 4,5). (a) Find L, the line of intersection of the two planes. (b) Suppose another line, L2, has vector equation (x, y, z) = (8,3,-2) + t2(-2, 1, 1). 6 marks] Find where Land L2 intersect 4 marks 3. Consider the two planes, P and P2, where Pi is given by the...