Find a point-normal equation of the plane passing through points A(1,-1,0), B(0, 0, 2) and C(0,3,1).
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.
Find an equation for the plane through the points (4,3,5), (1,0,-1), (0,2,-2). The Plane is?
Use the cross product to help find the normal form of the equation of a plane. 4. Use the cross product to help find the normal form of the equation of the plane. a. The plane passing through P= (1,0, –2), parallel to [0] u= 1 and v= -1 [ 2] b. The plane passing through P= (0,-1,1), Q = (2,0, 2), and R= (1, 2, -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.
Question 4 6-69) Consider the following three points: a-0 b-3and c-1 a) Find the parametric vector equation of the plane which passes through these three [3 marks] b) Find the vector cartesian equation of the plane passing through the three points listed [2 marks] c) Hence, or otherwise, find the non-vector cartesian equation of the plane passing through 3 marks] points above. the points above. Question 4 6-69) Consider the following three points: a-0 b-3and c-1 a) Find the parametric...
(41) find the equation of the plane passing through the points A(3,-2,0), B(2,0,3), and C(1,-1,1) in (i) vector form (ii) parametric form (iii) cartesian form
8. Find distance from point M to plane passing through A, B, C: M(-1, -6,3), A(0, -1, -1), B(-2,3,5), C(-1, -5, -9).
Find the plane through the points (1,0, 0), (0, 2,0), and (0,0,4)
--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).
find the point of intersection of the line 1) Find the equation of the line passing through the points A(1,-5,-3)and B(2,-4,8) (3 marks) b) Find the equation of the plane perpendicular to the line in part (a) given that C(1,-9,6) is a point on the plane. (3 marks) c) Find the point of intersection of the line and the plane in parts (a) and (b) above respectively. (3 marks)