Linear Algebra Let \(\vec{v} = \langle 2, 4, 3 \rangle\) and \(\vec{w} = \langle 5, 4, -4 \rangle\). Express the vector \(\vec{v}\) as the sum of a vector parallel to \(\vec{w}\) and a vector orthogonal to \(\vec{w}\).We denote the vector component of \(\vec{v}\) along \(\vec{w}\) as \(\vec{p}\), so \(\vec{p} = \text{proj}_{\vec{w}}\vec{v}\).We denote the vector component of \(\vec{v}\) orthogonal to \(\vec{w}\) as \(\vec{q}\), and have \(\vec{q} = \vec{v} - \vec{p}\), so that\[\vec{v} = \vec{p} + \vec{q}\](a) Determine the vector component of \(\vec{v}\) along \(\vec{w}\):\[\vec{p} = \](b) Determine the vector component of \(\vec{v}\) orthogonal to \(\vec{w}\):\[\vec{q} = \]Express all answers in exact form, no decimals.[Submit Question]

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Let = (2, 4,3) and =(5, 4, 4). Express the vector v as the sum of a vector parallel to w and a vector orthogonal to w. We denote the vector component of u along was p,so p = projzu. We denote the vector component of orthogonal to was , and have a-p, so that v=p+q. (a) Determine the vector component of v along w: p - - (b) Determine the vector component of orthogonal to w: q= Express all answers in exact form, no decimals. Submit Question

Let = (2, 4,3) and =(5, 4, 4). Express the vector v as the sum of a vector parallel to w and a vector orthogonal to w. We denote the vector component of u along was p,so p = projzu. We denote the vector component of orthogonal to was , and have a-p, so that v=p+q. (a) Determine the vector component of v along w: p - - (b) Determine the vector component of orthogonal to w: q= Express all answers in exact form, no decimals. Submit Question

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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