Let u, v, and w be vectors, and let a be a scalar. Prove the given property. (u + v) · w = u·w + v. w Let = (u1, u2), = (V1, v2), and w - (w1, w2). Then V = (lu1, u2) + (v1, v2)) · (w1, w2) ). (w1, w2) (u + v) · w = = U1W1 + V1W1 + %3D u1W1 + uzw2 + = (u1, u2) · ( (V1, v2) · %3D = u. W + v• w.
Let u, v, and w be vectors, and let a be a scalar. Prove the given property. (u + v) · w = u·w + v. w Let = (u1, u2), = (V1, v2), and w - (w1, w2). Then V = (lu1, u2) + (v1, v2)) · (w1, w2) ). (w1, w2) (u + v) · w = = U1W1 + V1W1 + %3D u1W1 + uzw2 + = (u1, u2) · ( (V1, v2) · %3D = u. W + v• w.
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 u, v, and w be vectors, and let a be a scalar. Prove the given property.
(u + v) · w = u·w + v. w
Let
(u1, u2), v = (vı1, v2), and w =
(W1, w2). Then
u =
(u + v) · w =
((u1, u2) + (v1, v2) · (w1, w2)
). (w1, w2)
= U1W1 + V1w1 +
- U1W1 + u2w2 +
= (u1, u2) · (
+ (V1, v2) ·
= u· W + v• W.
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