18. Find the equation of a plane that passes through the points (2, -2, 1), -1,...
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
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
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...
Q4. (5 points). Find the equation of the plane that passes through the line of intersection of the two planes x - 2y = 3 and y- z = 0 and parallel to the line x = y - 1 = 2+1 Q5. (4 points). Find the distance from the point A(1,2,3) and the line 2+1 y-1 2 Q6. (4 points). Give the name and sketch the surface whose equation is given by x2 + 2y2 – 12y – z...
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...
10. (8 points) Find the equation of the plane that passes through the points (1,-1, 1), (2,0,1) and (4,1,2)
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)
5. Find the equation of the plane which passes through the point (6,0,-2) and contains the line x = 4-2, y = 3 + 5t, and z 7+4t.
4.3 Find the equation of a plane that passes through (1,-2,4), (2,4,-4), and (1.25,-0.5, 2) using cross products and normal vectors. To find the equation of the plane, pick a point not on the plane.
Find an equation for the plane that passes through the points (2,0,1), (3,-1,2), and (1,1,2).