Here we use the formula to find the equation of the plane passing through three given points and get the result.
Find an equation for the plane that passes through the points (2,0,1), (3,-1,2), and (1,1,2).
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)
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
10. Write an equation for the plane containig the points (-7,2,1). (9.0,-2) and (-5, -1,2). Is this plane parallel, perpendicular or neither to the plane 2x - 3y + 2 = 5? 11. Consider the line that passes through the point (6, -5,2) and that is parallel to the vector (-1, 1, 3). (a) Find symmetric equations for this line (b) Find the point at which this line passes through the yz-plane.
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?
to the plane containing (-1,1,2), (9,2,0), and (3, 1,1) S2. Find the equation of the tangent plane to the graph of f(x,y)-sin(ry) at the point where r/3, y-1 to the plane containing (-1,1,2), (9,2,0), and (3, 1,1) S2. Find the equation of the tangent plane to the graph of f(x,y)-sin(ry) at the point where r/3, y-1
Find an equation for the line which passes through (-1,2) and is perpendicular to the line containing (0,2) and (4,6). The equation of the line is _______
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...
Find the normal form of the equation of the plane that passes through Find the vector form of the equation of the line in ℝ2 that passes through P = (5, −2) and is parallel to the line with general equation 5x − 4y = 2.