AI Tutor
Back to The cross product

Exercise 2.7.13

Avg difficulty 3.0

Which of the following systems of vectors u,v,w\mathbf{u},\mathbf{v},\mathbf{w} are right-handed? Which are left-handed? Which are coplanar?

  1. u=[1,0,1]T\mathbf{u}=\left[1,0,1\right]^{T}, v=[1,2,0]T\mathbf{v}=\left[1,2,0\right]^{T}, w=[0,0,1]T\mathbf{w}=\left[0,0,1\right]^{T}.

  2. u=[0,1,1]T\mathbf{u}=\left[0,1,1\right]^{T}, v=[−1,2,0]T\mathbf{v}=\left[-1,2,0\right]^{T}, w=[1,1,2]T\mathbf{w}=\left[1,1,2\right]^{T}.

  3. u=[1,−1,0]T\mathbf{u}=\left[1,-1,0\right]^{T}, v=[1,0,1]T\mathbf{v}=\left[1,0,1\right]^{T}, w=[3,1,4]T\mathbf{w}=\left[3,1,4\right]^{T}.

  4. u=[1,0,0]T\mathbf{u}=\left[1,0,0\right]^{T}, v=[1,2,0]T\mathbf{v}=\left[1,2,0\right]^{T}, w=[2,0,−1]T\mathbf{w}=\left[2,0,-1\right]^{T}.

Selinger, Matrix Theory and Linear Algebra, Vectors in Rn, The cross product, Exercise 2.7.13

AI Tutor

Adapted from Matrix Theory and Linear Algebra © 2017–2026 Peter Selinger, Lyryx Learning, and Ken Kuttler. Licensed under CC BY 4.0. Source: Matrix Theory and Linear Algebra. Imported at revision d74bc3a.