1. 2. Find an equation for the plane that is perpendicular to the plane 2.1 + y + 2z = 1 and contains the line Lor=2+t, y = 1+ 4t, z = 1+ 4t. Find the equation of the tangent plane to the surface 2z - 12 = 0 at the point (2,0,2).
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...
please explain thank you. 10. Find equation of the plane through the point (1,-1,-1) and parallel to the plane 5x – 3y – 2z = 6.
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...
please select the correct answer, thanks Describe the set of points zin the complex plane that satisfy the given equation: Iz-il = 12 +11 The line y = -X 1." 2. The line y = x 3. The line y = 2x 4. The line y = -2X QUESTION 17 Evaluate the given integral along the indicated contour. 2z)dz, where C is z(t)=t+ it?, ostsi 1.-12 +1 • 2.2 0 3.41 O 4.4
1. (15 points) (a) (5 points) Find the equation of the plane a that contains points A(1,5,4) B(1,0, 1) and C(4, 0,5) (b) (5 points) Find the distance from the point D(2, 1,7) to this plane (c) (5 points) If plane 3 has equation y -3z+2x = 5, find a unit vector that is parallel to the intersection of a and B.
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...
--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).
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.
Find the equation of the tangent line at the point (-3,2) to the curve defined implicitly below. y2 + 3y – 34 = -2x2 + 2x Select the correct answer below: O y = 2z+8 O y = 2x + 4 Oy-1-1 O y=+13 O y=-1-5 O y=x+5