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
6. Let P be the subspace in R 3 defined by the plane x − 2y + z = 0. (a) [5 points] Use the Gram–Schmidt process to find orthogonal vectors that form a basis for P. (b) [5 points] Find the projection p of b = (3, −6, 9) onto P. 6. Let P be the subspace in R3 defined by the plan 2y+z0 (a) [5 points] Use the Gram-Schmidt process to find orthogonal vectors that form a basis...
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
5e= 2y at the point (4, 8, 5) |Find the tangent plane to the equation z Preview xy at the point (6,8,10), and use it to approximate f(6.15, 8.19) 12 Find the linear approximation to the equation f(x, y) = 5, Preview f(6.15, 8.19) Make sure your answer is accurate to at least three decimal places, or give an exact answer 5e= 2y at the point (4, 8, 5) |Find the tangent plane to the equation z Preview xy at...
Find the orthogonal projection of; onto: =[.j, =[3] [9] ལ པ [3]
5. (a) Let u 1,4,2), ,1,0). Find the orthogonal projection of u on v (b) Letu ,1,0), u(0,1,1), (10,1). Find scalars c,,s such that 6. (a) Find the area of the triangle with vertices , (2,0,1), (3, 1,2). Find a vector orthogonal to the plane of the triangle. (b)) Find the distance between the point (1,5) and the line 2r -5y1 (i) Find the equation of the plane containing the points (1,2, 1), (2,1, 1), (1, 1,2). 7. (a) Let...
10. Find the volume of the solid under the plane x – 2y + z = 5 and above the region bounded by y = 1- x and y = 1-x2. Sketch the region of integration first!
Find the orthogonal projection of v⃗ 26 11 8 4 0 (1 point) Find the orthogonal projection ofv- 0 onto the subspace V of R spanned by and 28 (Note that these three vectors form an orthogonal set.) projv (u)-
Find an equation of a plane through the point (1, 5, 1) which is orthogonal to the line x=3+5t y=5-1t z=-1+4tin which the coefficient of x is 5.
Suppose we are looking for the point on the plane x + 2y + z = 5 closest to the point (2,3,0). Which of the following approaches DOES NOT lead to the answer? = 0 Solve the system of equationsJ 2(x - 2) - 2(5 - x - 2y) | 2(y-3) - 4(5 - x - 2y) = 0 Find the intersection point of the line r(t) = (2+ t, 3 + 2t, t) with the given plane. 2(x 2...
I need help with this question. I do not understand the role of the plane z=x+2y since boundary of x is [0,2] and y is [0,4]. Some concept clarification would be great. 2. (5 points) Sketch (rough sketch is ok) the solid that lies between the surface z r*+1 -0, x-2. У-0, and y-4 and the plane -x+2y and is bounded by the planes x Then, find its volume. 2. (5 points) Sketch (rough sketch is ok) the solid that...