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Let P be the plane that passes through the points (4,0,0), (0,4,0) and (0,0,2). Find 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.
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)
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 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...
Find an equation for the plane that passes through the points (2,0,1), (3,-1,2), and (1,1,2).
Find an equation of the plane with the given characteristics. The plane passes through (0, 0, 0), (2,0, 6), and (-3, -1, 9). Find the distance between the point and the plane. (0, 0, 0) 3x + 7y + z = 21 The position vector r describes the path of an object moving in space. Find the velocity v(t), speed s(t), and acceleration a(t), of the object. r(t) = ti + Rj+ K
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 an equation of the plane that passes through the point P(-2, -3,4) and has the vector n = (-8,7,2) as a normal. Edit III
In this problem, let li be the line that passes through the points A(1,2, 4) and B(-1,3,8), and let l2 be the line with symmetric equations x +1 = 2y = 32 — 3. Parts (e) and (f) relate to the vector field F = (xy, xz, yz). (a) Show that the lines li and l2 intersect. (b) Let P be the plane that contains both lines li and lz. Find an equation for P. (c) Show that the points...
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.