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 equati...
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...
(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
Find parametric equations of the plane that passes through the origin and has normal vector (3, 1, −6).
please answer question 16 and 17 17. Find the equation of a plane that passes through the points (15,5, 2), (6, 2, 1) and (10,3, 2). Does the point (-2,-5, -3) lie on the plane? [5 marks) 16. Find the equation of a line through the point (2, -3, 1) in a direction orthogonal to the line *+1 Y-1.2+2. Give your answer in both parametric and 3 5 symmetric form. [4 marks) 2
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.
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...
(1) (a) Find the equation of the line, Li, which passes through the points A : (4,y,z) = (0, -5, -3) and B : (x, y, z)=(3, 1,0). (b) Find the equation of the line, Ly, which passes through the points C:(x, y, z)=(-1, -3,2) and D: (x,y,z) = (4,3,6). (c) Show that L and Ly are not parallel lines. (d) Write the parametric equations for L, and L2, and then show that the lines Li and L2 do not...
18. Find the equation of a plane that passes through the points (2, -2, 1), -1, 0, 3) [5 marks] and (5,-3, 4). Does the point (2, 1, -3) lie on the plane?
Find the equation of a plane that passes through the points (2,-2,4), (1, 3,-2) and (5, 0, 1). Does the point (2, 3, -9) lie on the plane? 19. [5 marks] Assignment 2.1Bsp...pf Show All
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