(1 pt) Suppose u= <1,-2,-3> and v = <-1,-1,0>.
Then:
1. The projection of u along v is .
2. The projection of u orthogonal to v is
(1 pt) Suppose u= <1,-2,-3> and v = <-1,-1,0>. Then: 1. The projection of u along...
1 point) Suppose u(-5, 1,3) and v (0, -3-4. Then: 1. The projection of u along v is 2. The projection of u orthogonal to v is
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...
TETETTERE Find u xv. u = (0, 1, -6), v= (1, -1,0) Show that u x v is orthogonal to both u and v. (u X v) · u = (u x v) v = Need Help? Read It Talk to a Tutor Solond Answer with CamScanner
(Section 11.3) Find the projection of u onto v and find the vector component of u orthogonal to v for: u=8 i+2j v = (2, 1, -2)
26 or 28 or both
25 28, find the vector projection of u onto v. Then write u In ExcTe wo orthogonal vectors, one of which is projyu. Insum of two orthogonal vect as a sum of two 26. (3.-7),2, 6) 27, u(8, 5), v 28, 2, 8), v-(9,-3 29 and 30, find the interior angles of the triangle with
25 28, find the vector projection of u onto v. Then write u In ExcTe wo orthogonal vectors, one of...
(b) Consider u = (1, 2, 3), v = (-1, 2, -1), w = (-1,0, 2); 1 E R. Determine the value of 1 # 0 for which u, v and w are linearly dependent. Write down the corresponding equation of dependence. [6 marks]
Find the orthogonal projection of v=[1 8 9] onto the subspace V
of R^3 spanned by [4 2 1] and [6 1 2]
(1 point) Find the orthogonal projection of v= onto the subspace V of R3 spanned by 2 6 and 1 2 9 projv(v)
(1 point) Let W(s, t) = F(u(s, t), v(s, t)) where u(1,0) = 1, u,(1,0) = 2, 4(1,0) = 4 v(1,0) = -8,0,(1,0) = 3,0,(1,0) = -9 F.(1,-8) = -9, F,(1,-8) = -1 W (1,0) = W (1,0) =
Question 19: Linear Transformations Let S = {(u, v): 0 <u<1,0 <v<1} be the unit square and let RCR be the parallelogram with vertices (0,0), (2, 2), (3,-1), (5,1). a. Find a linear transformation T:R2 + R2 such that T(S) = R and T(1,0) = (2, 2). What is T(0, 1)? T(0,1): 2= y= b. Use the change of variables theorem to fill in the appropriate information: 1(4,)dA= S. ° Sºf(T(u, v)|Jac(T)| dudv JA JO A= c. If f(x, y)...
(7) Let V be a finite-dimensional vector space over F, and PE C(V) In this question, we will show that P is an orthogonal projection if and only if P2P and PP It may be helpful to recal that P is the orthogonal projection onto a subspace U if and only if (1) P is a projection, and (2) ran(P)-U and null(P)U (a) Prove that if P is an orthogonal projection, then P2P and P is self-adjoint Hint: To show...