Please describe the reasoning n 1. Find the equation of the line I which is parallel...
I cannot get i) or j) 3. (20 marks) Consider the parallel lines L, : x= -3 +8 2 [1] and L2: x = 0 + [2] 4. and 11 [3 -21 the planes P1 : 3x + 2y + 2z = -7 and P2 : 2.x – 2y - 2 = 11. (a) Find the equation of a plane in standard form containing both L, and L. (b) Find an equation of the line of intersection of P, and...
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...
Please I need help asap Find the point, P, at which the line intersects the plane. x= - 10-9t, y = - 3 + 5t, z=9-2t; 5x - 2y + 8z = 7 The point, P, at which the line intersects the plane is (7. (Simplify your answer. Type an ordered triple.)
(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...
I have attached the questions and the final solutions. Please do all of questions 7 and 8 7. Given the line L:x,y,z-2,2,3+1,-1,-3, the plane S 3x-2y+2z-7 and the point A 1,1,1 a) Find parametric equations of the line which contains the point A, intersects the line and which is parallel to the plane b) Find parametric equations of the lne which contains the point A and which intersects the line Lat the&angle a) Show that V" is a subspace of...
Find the equation of the plane through the point (-2,8,10) and parallel to the line x=1+t, y=2t, z=4-3t
In Exercises 21-22, give the equation of the line that is the intersection of the given planes. 21. p1: 3(x-2) +(y 1)+4z 0, and p2: 2(x-1)-2(y+3) +6(2-1) 0 In Exercises 23-26, find the point of intersection between the line and the plane. 26. line: (1,2, 3) +t (3, 5,-1), plane: 3x-2y- z=-4 In Exercises 27-30, find the given distances. 27. The distance from the point (1, 2,3) to the plane 3(x-1)+(y 2)+5(2-2) 0. In Exercises 21-22, give the equation of...
Find the equation of a line that is parallel to the line x=16 and contains the point (-7,8). The equation of the parallel line is(Type an equation.)
(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...
Please provide clear handwritings for answers and specific step by step explanations of questions 3 and 4. Thank you. 3. Are the plane 6z 3y - 4z-12 and line L 2, y 32t, z2-2t parallel? If so, find the distance between them. If they are not parallel, but are intersecting (at a single point), find the point of intersection. If they are none of the above, draw a cat. 4. The line r(t) = 〈1, 1,1〉 +t(1,3,-1) and the plane...