(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
(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...
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...
The plane passing through the 3 points A(4, -2, 1), B(4, -1,4) and C(1,-4,2) can be expressed as a parametric vector equation of the form x a 1V+ 12v2 where 1 and d2 are real parameters. You are given that V1 Find suitable vectors a and V2 and enter them in the boxes below. You must enter your answers using Maple notation, for example, the vector \(\begin{pmatrix}1\2\\3\end{pmatrix} is entered as <1, 2, 3>. a = Your response Correct response No...
2. Let A:(-1,1,-1), B:(2,0.2), C:(4.1.-3), and D:(-3, 1, 10) be points in R. (a) Find the angles (in degrees) of the triangle with vertices A, B and C. (b) Find an equation of the plane passing through the points A, B, and C. (c) Find two unit vectors perpendicular the plane through A, B, and C. (d) Find the volume of the tetrahedron with vertices A, B, C, D. 3. (a) Find an equation of the tangent line to the...
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.
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.
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...
(a). Find the equation of the plane through Po = (1,2,1) with normal vector i = (3,1,2) (b). Find the equation of a plane through Po = (2,3,1) and parallel to the plane P:3x + 2y -- z = 4 | Q4. Consider the line z-3 y-2 3 L, : * - - - L2: **** 2+5 y-3 -1 2 (i). Write the equations of both lines in parametric form (ii). Find the direction vectors V1, V2 of the lines...
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)
Find a point-normal equation of the plane passing through points A(1,-1,0), B(0, 0, 2) and C(0,3,1).