Let a = (-5, 9, 2) and b = (-10, 3, –10) be vectors. Find the scalars and vectors defined below. Note that these formulas only depend on â = a the unit ||a|| vector in the direction of a. The component of b along a: comp, b = â · b = The projection of b onto a: (Note: you can write this without square roots.) Pab = (â · b)â=( The projection of b orthogonal to a: (This is defined in terms of the previous projection.) Pb =b – Pab = ( Hint: The meaning of these projections is seen from examples where a = i= (1,0, 0). comp; (2, 1, 5) = 2, P;(2, 1, 5) = (2,0, 0), and Pt (2, 1, 5) = (0, 1, 5)

Let a = (-5, 9, 2) and b = (-10, 3, –10) be vectors. Find the scalars and vectors defined below. Note that these formulas only depend on â = a the unit ||a|| vector in the direction of a. The component of b along a: comp, b = â · b = The projection of b onto a: (Note: you can write this without square roots.) Pab = (â · b)â=( The projection of b orthogonal to a: (This is defined in terms of the previous projection.) Pb =b – Pab = ( Hint: The meaning of these projections is seen from examples where a = i= (1,0, 0). comp; (2, 1, 5) = 2, P;(2, 1, 5) = (2,0, 0), and Pt (2, 1, 5) = (0, 1, 5)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

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Vectors and the Geometry of Space

Let a = (-5, 9, 2) and b = (-10, 3, –10) be vectors. Find the scalars and vectors defined below. Note that these formulas only depend on â
the unit
vector in the direction of a.
The component of b along a:
comp, b = â · b =
The projection of b onto a: (Note: you can write this without square roots.)
Pab = (â · b)â =
(
The projection of b orthogonal to a: (This is defined in terms of the previous projection.)
Pab = b – Pab = {
Hint: The meaning of these projections is seen from examples where a = i= (1, 0, 0).
comp; (2, 1, 5) = 2,
P;(2, 1, 5) = (2, 0, 0), and
P (2, 1, 5) = (0, 1, 5)

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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