Let a = (10,-1,1) and b = (5,-3,-9) be vectors.How do I find what the image is asking for? (A) Find the scalar projection of b onto a.Scalar Projection:(B) Decompose the vector b into a component parallel to a and a component orthogonal to a.Parallel component:Orthogonal Component:

(A) ⇒Projb→a→=a→·b→a→⇒Projb→a→=(10, -1, 1)·(5, -3,…

Answered: Let a = (10,-1,1) and b = (5,-3,-9) be…

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Let a = (10,-1,1) and b = (5,-3,-9) be vectors. How do I find what the image is asking for?

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.1: Length And Dot Product In R^n

Problem 83E: Guided Proof Prove that if u is orthogonal to v and w, then u is orthogonal to cv+dw for any scalars...

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Concept explainers

Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.

Question

Let a = (10,-1,1) and b = (5,-3,-9) be vectors.

How do I find what the image is asking for?

(A) Find the scalar projection of b onto a.
Scalar Projection:
(B) Decompose the vector b into a component parallel to a and a component orthogonal to a.
Parallel component:
Orthogonal Component:

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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