Find (u, v), ||u|l, ||v||, and d(u, v) for the given inner product defined on R". u = (1, 1, 1), (5, 2, 5), (u, v) = u1V1 + 2u2v2 + U3V3 V = (a) (u, v) (b) |lu|| (c) ||v|| (d) d(u, v)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Find \(\langle \mathbf{u}, \mathbf{v} \rangle\), \(\|\mathbf{u}\|\), \(\|\mathbf{v}\|\), and \(d(\mathbf{u}, \mathbf{v})\) for the given inner product defined on \(\mathbb{R}^n\).

\[
\mathbf{u} = (1, 1, 1), \quad \mathbf{v} = (5, 2, 5)
\]

\[
\langle \mathbf{u}, \mathbf{v} \rangle = u_1v_1 + 2u_2v_2 + u_3v_3
\]

(a) \(\langle \mathbf{u}, \mathbf{v} \rangle\)

\[
\boxed{}
\]

(b) \(\|\mathbf{u}\|\)

\[
\boxed{}
\]

(c) \(\|\mathbf{v}\|\)

\[
\boxed{}
\]

(d) \(d(\mathbf{u}, \mathbf{v})\)

\[
\boxed{}
\]
Transcribed Image Text:Find \(\langle \mathbf{u}, \mathbf{v} \rangle\), \(\|\mathbf{u}\|\), \(\|\mathbf{v}\|\), and \(d(\mathbf{u}, \mathbf{v})\) for the given inner product defined on \(\mathbb{R}^n\). \[ \mathbf{u} = (1, 1, 1), \quad \mathbf{v} = (5, 2, 5) \] \[ \langle \mathbf{u}, \mathbf{v} \rangle = u_1v_1 + 2u_2v_2 + u_3v_3 \] (a) \(\langle \mathbf{u}, \mathbf{v} \rangle\) \[ \boxed{} \] (b) \(\|\mathbf{u}\|\) \[ \boxed{} \] (c) \(\|\mathbf{v}\|\) \[ \boxed{} \] (d) \(d(\mathbf{u}, \mathbf{v})\) \[ \boxed{} \]
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