1. Find the projection and reflection of the point (1,2,3) with respect to the plane defined by x-3y+z=30
Solution-
1. Find the projection and reflection of the point (1,2,3) with respect to the plane defined...
Find the equation of the line passing through the point (1,2,3), and perpendicular to the plane x + y + z = 6.
(1 point) Find the mass of the solid bounded by the xy-plane, yz-plane, z-plane, and the plane (z/8) 1, if the density of the solid is given by o(r, y, z) = x + 3y (r/2)(y/4) mass
4. Find the orthogonal projection of 21 +J on the plane-x + 2y+ z = 5
4. Find the orthogonal projection of 21 +J on the plane-x + 2y+ z = 5
Question 9: Plane through point and line A plane contains the point P(-1,2,3) and the line L(t), where L(t) is given by equation (2, 4t - 3,1 – 4t). Find the equation of this plane. Type in the equation of the plane with the accuracy of at least 3 significant figures for each coefficient 1 ) x + ( Dy+ ( )= / Save & Grade Save only
3. Find the Kernel and the Range for the projection operator onto the plane z = 0 in the basis 7,J,K
3. Find the Kernel and the Range for the projection operator onto the plane z = 0 in the basis 7,J,K
1. Find the tangent plane to the given surface at the given point (1) z r'--yz? + уз at (1, 1, 1) (2)T at (2,3, 1) z+y+1 (3)2V +y at (1,2,3)
Question 9 Using Lagrange multipliers, find the point on the plane x + 3y + 72 = 1 that is closest to the origin. Enter the exact answers as improper fractions, if necessary. (x, y,z) = Edit ? Edit ? Edit
5. (a) Show that the point Q(1,0,0) lies in the plane x + y + z = 1 and the point P(1, -2,4) does not. (b) Find both the scalar and vector projections of the vector PQ onto the vector a = (1,1,1). (c) Use the scalar projection in (b) to find the distance from the point P(1, -2, 4) to the plane x+y+z=1.
Find the tangent plane to the equation z 2y cos(5x – 3y) at the point (3,5,10) z =
(5) Equations for Planes. (a) Find an equation of the plane passing through (1,2,3) that is parallel to the plane r -y + 2z = 5. (b) Find an equation of the plane passing through the point (0,1,0) and containing the line r = (-t, 2t, 4t).