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09: Find the equation of the plane that passes through (1,1,1) and has (-1,2,4) as normal....
Find the equation of the plane that passes through the ine of intersection of planes x+z=1 and y+2z=3 and is orthogonal to the plane x+y+z=34256. Express your answer in general form.
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.
(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...
Find the equation of the line passing through the point (1,2,4) and perpendicular to the plane x−y + z = 3
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)
please show work? CCC4 9.5.032. Find an equation of the plane. The plane that passes through the line of intersection of the planes - 22 and y + 32 - 3 and is perpendicular to the plane x + y - 425 Shu War
Find the equation for a plane containing 3 points: A(2, 2,1) in the form: ax+by+cz+d = 0 C(0, -2,1). Put the plane equation B(3,1, 0) х — 3 z+2 = y+5 = 2 L: Find the intersection point between 2 lines whose symmetric equations are: 4 х-2 L, : у-2 = z-3 -3 Find the parametric equation for a line that is going through point A(2,4,6) and perpendicular to the plane 5х-3у+2z-4%3D0. Name: x-3y4z 10 Find the distance between 2...
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...
--1)+3y+2(z-4) 0 (9) Find an equation of the plane (a) through the point (2,0, 1) and perperndicular to the line a =3t, y 2- t,z3t+4 (b) passes through the point (1,-1,-1) parallel t the plane bz-y-z6 (c) passes through the point (3,5,-1) and contains the line a 4-t,y = -1+2t, z3t (d) passing through (-1,1,1), (0,0,2) and (3,-1,-2).
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