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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Transcribed Image Text: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)
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