Let k ⊂ R 3 be the plane given by the equation ax+by+cz=d,
can plane k written or express as a span of a set vectors? Justify your answer.
Let k ⊂ R 3 be the plane given by the equation ax+by+cz=d, can plane k...
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...
(1) Equation of a Plane Let P(1,1,-1), Q(1,2,0), R(-2,2,2). (la) Compute PQxPR. (1b) Find the equation of the plane through P, Q and R in the form ax+by+cz=d. (10) What is the angle formed by this plane and the xy-plane?
Let P(0,1,0), Q(2,1,3), R(1,-1,2). (la) Compute PQxPR. (1b) Find the equation of the plane through P, Q and R in the form ax+by+cz=d (10) What is the angle formed by this plane and the xy-plane? Please answer ic.
Consider the plane ax + by + cz=d. Determine a parameterization 7(u, v) of the surface (assume that c is not 0), and show that we always get that the magnitude/length of rury is a constant (and therefore the surface area can always be represented as a double integral of a constant).
a. Every matrix equation Ax b corresponds to a vector equation with the same solution set. Choose the correct answer below. O A. False. The matrix equation Ax-b does not correspond to a vector equation with the same solution set. O B. False. The matrix equation Ax b only corresponds to an inconsistent system of vector equations. O c. True. The matrix equation Ax-bis simply another notation for the vector equation x1a1 + x2a2 +·.. + xnan-b, where al ,...
3. Find the equation of the tangent plane to the surface 3 at the point (-2,1,-3). Write your final answer in the form ax + by + cz =d, such that all coefficients are integers.
3. Let S be the plane through the points A(0,0,-1), B(0,2,0), C(3,0,0). (a) Find an equation for S of the form ax +by+cz = d. (b) Find the point on that is closest to the point P(2,2,3).
Find an equation of the tangent plane to the following parametric surface, r(u, v) = (u2 + 9) i + (v3 + 6u) j + (u + 2v) k , at the point (10, 5, −1). Write the equation in the form ax + by + cz + d = 0, where a, b, c, and d have no common factors. Then enter the values of a, b, c, and d (in that order) into the answer box below, separated...
Let A be an m × n matrix, let x Rn and let 0 be the zero vector in Rm. (a) Let u, v є Rn be any two solutions of Ax 0, and let c E R. Use the properties of matrix-vector multiplication to show that u+v and cu are also solutions of Ax O. (b) Extend the result of (a) to show that the linear combination cu + dv is a solution of Ax 0 for any c,d...
(a) Let A be a fixed mx n matrix. Let W := {x ER" : Ax = 0}. Prove that W is a subspace of R". (b) Consider the differential equation ty" – 3ty' + 4y = 0, t> 0. i. Let S represent the solution space of the differential equation. Is S a subspace of the vector space C?((0.00)), the set of all functions on the interval (0,0) having two continuous derivatives? Justify ii. Is the set {tº, Int}...