8. Find distance from point M to plane passing through A, B, C: M(-1, -6,3), A(0,...
Find a point-normal equation of the plane passing through points A(1,-1,0), B(0, 0, 2) and C(0,3,1).
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.
Q4 (8 points) (a) Find parametric equations to the line passing through the point A(5,-2,9) and perpendicular to the plane 3x - y - 6x + 2 = 0 (b) Find two planes that intersect along the line.
Q4 (8 points) (a) Find parametric equations of the line passing through the point A(5,-2,9) and perpendicular to the plane 33 - Y --- 62 +2 = 0. (b) Find two planes that intersect along the line
--1)+3y+2(z-4) 0 (9) Find an equation of the plane (a) through the point (2,0, 1) and perperndicular to the line a =3t, y 2- t,z3t+4 (b) passes through the point (1,-1,-1) parallel t the plane bz-y-z6 (c) passes through the point (3,5,-1) and contains the line a 4-t,y = -1+2t, z3t (d) passing through (-1,1,1), (0,0,2) and (3,-1,-2).
Q4 (8 points) (a) Find parametric equations of the line passing through the point A(5,-2,9) and perpendicular to the plane 3.x - y-6z+ 2 = 0. (b) Find two planes that intersect along the line.
(5) Equations for Planes. (a) Find an equation of the plane passing through (1,2,3) that is parallel to the plane r -y + 2z = 5. (b) Find an equation of the plane passing through the point (0,1,0) and containing the line r = (-t, 2t, 4t).
5) Find the equation for the tangent plane passing through the point (3, 1,0) for the function: z = ln(x – 2y) Please put your final answer in the form z = ax +by+ c, where a, b, and c are real valued constants.
Question 3 a) Find the cartesian equation of the line that passes through the origin and lies perpen- (3 dicular to the plane 3x - 5y +2z 8. marks] b) Find the cartesian equation of the plane that lies perpendicular to the line 3 marks] and passes through the point 1 cExplain why a unique plane passing through the three points A(-2,-1,-4), B(0,-3,0) [2 marks) and C(2,-5,4) cannot be defined. Question 3 a) Find the cartesian equation of the line...