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Exercise 3

Avg difficulty 2.5

Suppose that v\vvec and w\wvec are vectors where v⋅v=4,w⋅w=20,v⋅w=8.\vvec\cdot\vvec = 4, \hspace{24pt} \wvec\cdot\wvec = 20,\hspace{24pt} \vvec\cdot\wvec=8.

  1. What is ∣v∣\len{\vvec}?

  2. What is the angle between v\vvec and w\wvec?

  3. Suppose that tt is a scalar. Find the value of tt for which v\vvec is orthogonal to w+tv\wvec+t\vvec?

Austin, Understanding Linear Algebra, §6.1 The dot product, Exercise 3

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Adapted from Understanding Linear Algebra © 2023 David Austin. Licensed under CC BY 4.0. Source: Understanding Linear Algebra. Imported at revision 3e6dced.