(1 point) Let a = <4, 10, -4> and b = <-8, 4, 1> be vectors. Find the scalar and vector projections of b onto a.
(2) Use projections onto the 8 basis vectors you got in (1) to decomposo the vector xint parallel and orthogonal components tospan(b) We were unable to transcribe this image (2) Use projections onto the 8 basis vectors you got in (1) to decomposo the vector xint parallel and orthogonal components tospan(b)
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.
11 -14 (1 point) Let W be the subspace of R3 spanned by the vectors 1 and 4 Find the projection matrix P that projects vectors in R3 onto W
8. Let W be the set of all vectors in R3 of the form a(8, 9, 1), where a is a real number. A. Let b and c be arbitrary real numbers such that b(8, 9, 1) and c(8, 9, 1) are in W. Is b(8, 9, 1) + c(8, 9, 1) in W? B. Let k be a scalar and let b be an arbitrary real number such that b(8, 9, 1) is in W. Is k(b(8,9,1)) in W?...
For parts ( a ) − ( c ), let u = 〈 2 , 4 , − 1 〉 and v = 〈 4 , − 2 , 1 〉. ( a ) Find a unit vector which is orthogonal to both u and v. ( b ) Find the vector projection of u onto v. ( c ) Find the scalar projection of u onto v.
6 ture Supplement 4: Intro Vectors Worksheet B a vector (graphical, verbal, or mathematical) that is in: Provide an example of a) ID b) 2D c) 3D (graphi Outline the main vector operations we will use in class: a) Vector Addition b) Vector Subtraction c) Scalar Multiplication d) Vector Dot Product e) Vector Cross Product What is a resultant vector? 4 What is the component of a vector? 3,Define a unit vector. Give an example of a unit vector in...
(1 point) Let W be the subspace of R spanned by the vectors 27 1 and -7 Find the matrix A of the orthogonal projection onto W. A =
Problem 5. (1 point) Let H be the subset of vectors [x. y] in R2 such that the polint (x, y) les between the lines y -3x and y x/3. (See the picture.) 1. Is H nonempty? choose 2. Is H closed under addition? If it is, enter CLOSED. If it is not, enter two vectors in H whose sum is not in H, using a comma separated list and syntax such as [1.2]. 13,4] 3 Is H closed under...
2) 3) If a = (2, -1, 2) and b = (9, 2, 1), find the following. a xb -6i + 16 + 13k x b xa = 6i – 16j – 13k x Need Help? Read It Watch It Talk to a Tutor Find the scalar and vector projections of b onto a. a = (4,7,-4) b = (3, -1, 1) scalar projection of b onto a 1 9 vector projection of b onto a Find, correct to the...
6. 2D vectors Lec ture Supplement 4: Intro Vectors Worksheet B Provide an example of a) ID b) 2D c) 3D a vector (graphical, verbal, or mathematical) that is in: (graphi Outline the main vector operations we will use in class: a) Vector Addition b) Vector Subtraction c) Scalar Multiplication d) Vector Dot Product e) Vector Cross Product What is a resultant vector? 4 What is the component of a vector? &Define a unit vector. Give an example of a...