Question

Let ε₁ and ε₂ be the angles made by  \[\vec{A}\] and -\[\vec{A}\] with the positive X-axis. Show that tan ε₁ = tan ε_2. Thus, giving tan ε does not uniquely determine the direction of \[\vec{A}\].

  

Answer 1

The direction of - \[\vec{A}\] is opposite to \[\vec{A}\].So, if vector \[\vec{A}\] and \[- \vec{A}\] make the angles ε₁ and ε₂ with the X-axis, respectively, then ε₁ is equal to ε₂ as shown in the figure:

Here, tan ε₁ = tan ε₂
Because these are alternate angles.
Thus, giving tan ε does not uniquely determine the direction of \[- \vec{A}\].