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The parallelogram determined by non-zero vectors 7 and w has the same area as the parallelogram determined by 7 and 7+ w. If and w are non-zero vectors satisfying v × w = 0, then is a scalar multiple of w. If u, v and w are non-zero vectors satisfying u x =ux w, then v = w.

The parallelogram determined by non-zero vectors 7 and w has the same area as the parallelogram determined by 7 and 7+ w. If and w are non-zero vectors satisfying v × w = 0, then is a scalar multiple of w. If u, v and w are non-zero vectors satisfying u x =ux w, then v = w.

Advanced Engineering Mathematics
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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Determine whether these statements are true or false
The parallelogram determined by non-zero vectors \(\vec{v}\) and \(\vec{w}\) has the same area as the parallelogram determined by \(\vec{v}\) and \(\vec{v} + \vec{w}\). If \(\vec{v}\) and \(\vec{w}\) are non-zero vectors satisfying \(\vec{v} \times \vec{w} = \vec{0}\), then \(\vec{v}\) is a scalar multiple of \(\vec{w}\). If \(\vec{u}\), \(\vec{v}\), and \(\vec{w}\) are non-zero vectors satisfying \(\vec{u} \times \vec{v} = \vec{u} \times \vec{w}\), then \(\vec{v} = \vec{w}\).
Transcribed Image Text:The parallelogram determined by non-zero vectors \(\vec{v}\) and \(\vec{w}\) has the same area as the parallelogram determined by \(\vec{v}\) and \(\vec{v} + \vec{w}\). If \(\vec{v}\) and \(\vec{w}\) are non-zero vectors satisfying \(\vec{v} \times \vec{w} = \vec{0}\), then \(\vec{v}\) is a scalar multiple of \(\vec{w}\). If \(\vec{u}\), \(\vec{v}\), and \(\vec{w}\) are non-zero vectors satisfying \(\vec{u} \times \vec{v} = \vec{u} \times \vec{w}\), then \(\vec{v} = \vec{w}\).
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