Question

For which angle(s) $\mathit{\theta }$ can you find three distinct unit vectors in${\mathbf{ℝ}}^{\mathbf{2}}$ such that the angle between any two of them is$\mathit{\theta }$ ? Draw a sketch.

Short answer

The Angle is $\theta ={120}^0$

Step-by-step solution

The Eigenvector

• An eigenvector or characteristic vector of a linear transformation is a nonzero vector that changes by no more than a scalar factor when that linear transformation is applied to it.
• The factor by which the eigenvector is scaled is represented by the associated eigenvalue, which is frequently denoted by lambda.

Determine the angle

The angle must add up to$2\pi rad={360}^0$(measure of one complete cycle), and the angle for which we can find three distinct eigenvectors in${\mathrm{ℝ}}^2$is given by

$\theta =\frac{360}{3}={120}^0$The sketch is shown below.