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

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Let = (2, 4, 3) and = (5, 4, 4). Express the vector as the sum of a vector parallel to w and a vector orthogonal to w. We denote the vector component of v along was p, so p = projv. We denote the vector component of orthogonal to was ad, and have a = - p , so that v=p+q. (a) Determine the vector component of u along w: р = (b) Determine the vector component of orthogonal to w: q = 1 Express all answers in exact form, no decimals. Submit Question

Let = (2, 4, 3) and = (5, 4, 4). Express the vector as the sum of a vector parallel to w and a vector orthogonal to w. We denote the vector component of v along was p, so p = projv. We denote the vector component of orthogonal to was ad, and have a = - p , so that v=p+q. (a) Determine the vector component of u along w: р = (b) Determine the vector component of orthogonal to w: q = 1 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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