Find the decomposition a = a|| + a₁ with respect to b if a = (3, 4, 2), b = (3, 4, 6).= (a||x, a||y, a||z)a¹b =(alx, aly, alz)(Enter the components of vectors using symbolic notation and fractions where needed.)a||xallya||zab ===alx =aly =alz =

Given: a→=3,4,2and b→=3,4,6 To find: Decomposition a=a∥+a⊥with respect to b. Here,…

Answered: Find the decomposition a = a + a₁ with…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

Find the decomposition a = a|| + a₁ with respect to b if a = (3, 4, 2), b = (3, 4, 6).
= (a||x, a||y, a||z)
a¹b =
(alx, aly, alz)
(Enter the components of vectors using symbolic notation and fractions where needed.)
a||x
ally
a||z
ab =
=
=
alx =
aly =
alz =

Expert Solution

Step 1

Given: $\vec{a} = <3, 4, 2>$ and $\vec{b} = <3, 4, 6>$

To find:

Decomposition $a = a_{∥} + a_{⊥}$ with respect to $b$ .

Here,

$a_{∥ b} = <a_{∥ x}, a_{∥ y}, a_{∥ z}> a_{⊥ b} = <a_{⊥ x}, a_{⊥ y}, a_{⊥ z}>$

Formula Used:

${\vec{a}}_{∥ \vec{b}} = {proj}_{b}^{a} = \frac{\vec{a} . \vec{b}}{{|b|}^{2}} . \vec{b} {\vec{a}}_{⊥ \vec{b}} = a - {\vec{a}}_{∥ \vec{b}}$

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Find the decomposition a = a + a₁ with respect to b if a = (3,4,2), b = (3, 4, 6). ab = (a||x, a|ly, a||z) ab = (α₁x, аly, alz) (Enter the components of vectors using symbolic notation and fractions where needed.) al|x ally = allz = alx = aly = alz = 11